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Sheryl Sandberg, the chief operating officer of Meta and the longtime second in command to its founder, Mark Zuckerberg, said on Wednesday that she was stepping down from the company after 14 years.

Ms. Sandberg said she was leaving Meta this fall and that she planned to continue serving on the company’s board of directors. Meta owns Facebook, Instagram, WhatsApp and other apps.

“When I took this job in 2008, I hoped I would be in this role for five years. Fourteen years later, it is time for me to write the next chapter of my life,” Ms. Sandberg wrote in a Facebook post.

She added that she was “not entirely sure what the future will bring” but that she would focus on her foundation and philanthropy. Ms. Sandberg also said she was getting married this summer.

Ms. Sandberg served as the key lieutenant to Mr. Zuckerberg at Facebook, which she joined after building the advertising business at Google. Ms. Sandberg was often cited as being the adult in the room during Facebook’s early days, tasked with turning a fast-growing start-up into a profitable enterprise.

This is a developing story. Check back for updates.

WASHINGTON — The Russian military, beaten down and demoralized after three months of war, is making the same mistakes in its campaign to capture a swath of eastern Ukraine that forced it to abandon its push to take the entire country, senior American officials say.

While Russian troops are capturing territory, a Pentagon official said that their “plodding and incremental” pace was wearing them down, and that the military’s overall fighting strength had been diminished by about 20 percent. And since the war started, Russia has lost 1,000 tanks, a senior Pentagon official said last week.

President Vladimir V. Putin of Russia appointed a new commander, Gen. Aleksandr V. Dvornikov, in April in what was widely viewed as an acknowledgment that the initial Russian war plan was failing.

Soon after his arrival, General Dvornikov tried to get disjointed air and land units to coordinate their attacks, American officials said. But he has not been seen in the past two weeks, leading some officials to speculate as to whether he remains in charge of the war effort.

Russian pilots also continue to demonstrate the same risk-averse behavior they did in the early weeks of the war: darting across the border to launch strikes and then quickly returning to Russian territory, instead of staying in Ukrainian air space to deny access to their foes. The result is that Russia still has not established any kind of air superiority, officials said.

The Russian military has made some progress in the east, where concentrated firepower and shortened supply lines have helped its forces fight intense battles in recent days. After three bloody months, Russia finally took Mariupol in mid-May, potentially creating a land bridge from the Russian-controlled Crimean Peninsula to the south.

As Russia struggles to move forward, Ukraine has also suffered setbacks. President Volodymyr Zelensky of Ukraine recently said that as many as 100 Ukrainian servicemen might be dying every day in the fighting. And on Tuesday, Russian troops advanced toward the center of Sievierodonetsk, a city that has become a central focus for the military since it shifted its attention to the east.

But some of the areas that Russian forces managed to seize have been quickly contested again, and sometimes retaken, by Ukrainian troops.

Consider Kharkiv. Russia spent six weeks bombarding the eastern city, once home to 1.5 million people, as troops encircled it.

But by May 13, control of the city had flipped again. “The Russians took Kharkiv for a short period of time; the Ukrainians counterattacked and took Kharkiv back,” Defense Secretary Lloyd J. Austin III said at a news conference at the Pentagon last week. “We’ve seen them really proceed at a very slow and unsuccessful pace on the battlefield.”

Ukraine is now pushing Russian troops north and east from Kharkiv, “in some cases all the way back to Russia,” said retired Gen. Philip Breedlove, the former supreme allied commander for Europe. “So now Ukrainians are threatening to cut off Russian lines of supply and pushing their forces to the rear.”

Cutting off Russian supply lines east of Kharkiv would put Russian troops in the same situation they were in after their advance on Kyiv, the capital of Ukraine, at the beginning of the war, officials said. Ukrainian units carrying shoulder-fired Javelin antitank missiles picked off Russian soldiers as miles-long Russian convoys near Kyiv stopped moving forward. The invasion stalled, and thousands of Russian troops were killed or injured. Russia then refocused its mission on the east.

In the early weeks of the war, Russia ran its military campaign out of Moscow, with no central war commander on the ground to call the shots, American and other Western officials said. In early April, after Russia’s logistics and morale problems had become clear, Mr. Putin put General Dvornikov in charge of a streamlined war effort.

General Dvornikov arrived with a daunting résumé. He started his career as a platoon commander in 1982 and later fought in Russia’s brutal second war in Chechnya. Moscow also sent him to Syria, where the forces under his command were accused of targeting civilians.

In Ukraine, he established a more streamlined process. Russian pilots began coordinating with troops on the ground toward a similar objective in the eastern region of Donbas, and Russian units were talking to one another about shared goals.

But the invasion is not “proceeding particularly differently in the east than in the west because they haven’t been able to change the character of the Russian army,” said Frederick W. Kagan, a senior fellow and director of the Critical Threats Project at the American Enterprise Institute. “There are some deep flaws in the Russian army that they could not have repaired in the last few weeks even if they had tried. The flaws are deep and fundamental.”

At the top of that list is the Russian army’s lack of a noncommissioned officers corps empowered to think for itself, Pentagon officials said. American troops have sergeants and platoon leaders and corporals who are given tasks and guidelines and left to accomplish those tasks as they see fit.

But Russia’s military follows a Soviet-style doctrinal method in which troops at the bottom are not empowered to point out flaws in strategy that should be obvious or to make adjustments.

The Ukrainians, after seven years of training alongside troops from the United States and other NATO countries, follow the more Western method and have proved particularly agile at adapting to circumstances, American military officials said.

A two-week fighting pause after the Russian military gave up the fight for Kyiv was not long enough to turn the campaign around, even with a more limited goal, General Breedlove said. General Dvornikov’s “new tactics, resetting the command and control so there was a focused decision maker — all that was right or proper,” he said.

But, General Breedlove added: “Even our army would be hard-pressed to refit, refurbish and reorganize in two weeks after having received such a sound whipping.” When General Dvornikov took control, “the force was thrust back into the battle too quickly. That decision had to have come from Moscow.”

After renewing an assault on the Donbas, Russia has pounded cities and villages with a barrage of artillery. But troops have not followed that up with any kind of sustained armored invasion, which is necessary if they will hold the territory they are flattening, military officials say. That means that Russia may find itself struggling to hold on to gains — as it did in Kharkiv.

Evelyn Farkas, a former senior Pentagon official for Ukraine and Russia in the Obama administration, said Mr. Putin was still too involved in the fight.

“We keep hearing accounts of Putin getting more involved,” said Ms. Farkas, who is now executive director of the McCain Institute. “We know that if you have presidents meddling in targeting and operational military decisions, it’s a recipe for disaster.”

Before invading Ukraine on Feb. 24, Russian forces already controlled about 30 percent of the eastern Ukrainian region known as Donbas. Russia had taken the territory — with help from local separatist forces — as part of a sporadic, often low-grade war with Ukraine that began in 2014.

Today, Russia controls closer to 75 percent of Donbas. Some of the most recent Russian gains have come around Sievierodonetsk.

Together, those two statistics — 30 percent and 75 percent — offer a useful summary of the war.

Yes, the war has gone much worse for Russia than almost anybody expected: Rather than overrunning Kyiv, Ukraine’s capital, in mere days, the Russian military had to backtrack and narrow its goals to Donbas, a long-disputed border region. But Russia is nonetheless making progress there. It may yet accomplish the more limited goal of dominating Donbas. And Vladimir Putin is betting that he will prove more patient than Ukraine’s Western allies.

Today’s Times has several notable pieces of Ukraine coverage. Helene Cooper looks at the military mistakes that Russia is repeating, and Carlotta Gall profiles the Ukrainians choosing to stay in their homes in Donbas. Three photographers — Lynsey Addario, Finbarr O’Reilly and Ivor Prickett — have published images and stories from the front lines.

In the Opinion section, President Biden has published an essay explaining that his administration will continue to send weapons to Ukraine but not troops. In the essay, he announces that the U.S. will send longer-range missiles to Ukraine than it previously has.

Alongside those pieces, we’re using today’s newsletter to give you an overview of the war.

A Russian pincer

The big question over the next several weeks — according to our colleague Julian Barnes, who covers U.S. intelligence agencies — will be whether Russia can encircle Ukraine’s forces in Donbas. If Russia can, the Ukrainian troops could be cut off from the rest of the country and suffer heavy losses. Russia might then be in position to take control of nearly all of Donbas.

“Intelligence officials have repeatedly said, both publicly and privately, that this next phase is going to be very important in setting the tenor for the war in the months to come,” Julian said. “It will determine whether we stay in something approximating a stalemate or if one side gets the upper hand.”

In the war’s early weeks, Russia tried to move quickly and capture large sections of territory. Its military proved incapable of doing so, rebuffed by Ukrainian troops, with help from weapons provided by the U.S., E.U. and other allies. In the war’s current phase, Russia has emphasized a strategy from other recent wars, in Syria and Chechnya: using missiles and other heavy artillery to bombard cities and towns and eventually take them over.

As Anton Troianovski, The Times’s Moscow bureau chief, says: “The war has clearly gone on much longer than anyone anticipated, including the Russians. And the Russians after those initial failures have adapted and have gone back to the traditional method of fighting wars.”

The bombardment appears to be causing substantial Ukrainian casualties. On a typical recent day, between 50 and 100 Ukrainian troops were killed, President Volodymyr Zelensky recently estimated. Russia has also managed to capture some economically significant areas, including ports and wheat fields.

Putin has adopted a strategy that Russia has used for much of its history, combining its vast resources with a high tolerance of casualties to make slow wartime gains. In this war, Putin believes that Ukraine’s Western allies become weary of the fight long before he feels much pressure to do so. “He’s betting on the West to get tired and to get distracted,” Anton said.

Still, Putin faces many of the same problems that undermined Russia’s initial invasion, as Helene Cooper’s story explains. Its military has proved to be an inefficient, top-down organization in which field commanders often must wait for high-level orders. Much of Russia’s equipment is out of date, and many of its troops are not well trained. They also did not expect to be part of a full-scale war, and the deaths of thousands of their fellow soldiers have further weakened morale.

“The Russians are attempting to subdue a massive country with a well-organized military that is fighting on its home turf,” Helene said. “That is a very tall order for an army where you have soldiers on the ground with no clue why they are even in Ukraine.”

Barriers to peace

Ultimately, many analysts believe that Russia’s military problems will make it very difficult for Putin to control large parts of Ukraine for months or years. Yet Donbas is where he is most likely to find some success.

“The overall military balance in this war still trends in Ukraine’s favor, given manpower availability and access to extensive Western military support,” Michael Kofman, the director of Russia studies at CNA, a research group, recently wrote. “That will show itself more over time. But the local balance in the Donbas during this phase is a different story.”

The most likely medium-term scenario is that Russia will control a large amount of Donbas and that Putin will patiently and brutally try to expand Russia’s holdings. He — as well as Ukraine and its allies — would then need to decide whether any truce is possible.

“I will not pressure the Ukrainian government — in private or public — to make any territorial concessions,” Biden wrote in his Times essay.

More on Ukraine

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The most watchable team in baseball

The Savannah Bananas, a collegiate summer-league baseball team in Georgia, have sold out every home game since 2016. They also have more TikTok followers than the Yankees and Mets combined. The dancing umpires might have something to do with that.

Bananas games are a bit like a circus, Margaret Fuhrer writes in The Times. Players will sometimes wear stilts. The first-base coach is a charismatic hip-hop dancer who has never played baseball. A cast of 120 entertainers — including a pep band and a “dad bod cheerleading squad” — adds to the spectacle.

“We want people who used to say, ‘I don’t like baseball,’ to say, ‘I have to see the Bananas,’” said Jesse Cole, the team’s owner, who also serves as the on-field host sporting a yellow tuxedo.

PLAY, WATCH, EAT

What to Cook

WASHINGTON — Michael Sussmann, a prominent cybersecurity lawyer with ties to Hillary Clinton’s presidential campaign, was acquitted on Tuesday of lying to the F.B.I. in 2016 when he shared a tip about possible connections between Donald J. Trump and Russia.

The verdict was a significant blow to the special counsel, John H. Durham, who was appointed by the Trump administration three years ago to scour the Trump-Russia investigation for any wrongdoing.

But Mr. Durham has yet to fulfill expectations from Mr. Trump and his supporters that he would uncover and prosecute a “deep state” conspiracy against the former president. Instead, he has developed only two cases that led to charges: the one against Mr. Sussmann and another against a researcher for the so-called Steele dossier, whose trial is set for later this year.

Both consist of simple charges of making false statements, rather than a more sweeping charge like conspiracy to defraud the government. And both involve thin or dubious allegations about Mr. Trump’s purported ties to Russia that were put forward not by government officials, but by outside investigators.

The case against Mr. Sussmann centered on odd internet data that cybersecurity researchers discovered in 2016 after it became public that Russia had hacked Democrats and Mr. Trump had encouraged the country to target Mrs. Clinton’s emails.

The researchers said the data might reflect a covert communications channel using servers for the Trump Organization and Alfa Bank, which has ties to the Kremlin. The F.B.I. briefly looked at the suspicions and dismissed them.

On Sept. 19, 2016, Mr. Sussmann brought those suspicions to a senior F.B.I. official. In charging Mr. Sussmann with a felony, prosecutors contended that he falsely told the official that he was not there on behalf of any client, concealing that he was working for both Mrs. Clinton’s campaign and a technology executive who had given him the tip.

Mr. Durham and prosecutors used court filings and trial testimony to describe how Mr. Sussmann, while working for a Democratic-linked law firm and logging his time to the Clinton campaign, had been trying to get reporters to write about the Alfa Bank suspicions.

But trying to persuade reporters to write about such suspicions is not a crime. Mr. Sussmann’s guilt or innocence turned on a narrow issue: whether he made a false statement to the senior F.B.I. official at the 2016 meeting by saying he was sharing those suspicions on his own.

Mr. Durham used the Sussmann case to put forward a larger conspiracy: that there was a joint enterprise to essentially frame Mr. Trump for collusion with Russia by getting the F.B.I. to investigate the suspicions so reporters would write about it. The scheme, Mr. Durham implied, involved the Clinton campaign; its opposition research firm, Fusion GPS; Mr. Sussmann; and the cybersecurity expert who had brought the odd data and analysis to him.

That insinuation thrilled Mr. Trump’s supporters, who have embraced his claim that the Russia investigation was a “hoax” and have sought to conflate the official inquiry with sometimes dubious accusations. In reality, the Alfa Bank matter was a sideshow: The F.B.I. had already opened its inquiry on other grounds before Mr. Sussmann passed on the tip; the final report by the special counsel, Robert S. Mueller III, made no mention of the Alfa Bank suspicions.

But the case Mr. Durham and his team used to float their broad insinuations was thin: one count of making a false statement in a meeting with no other witnesses. In a rebuke to Mr. Durham; the lead lawyer on the trial team, Andrew DeFilippis; and his colleagues, the 12 jurors voted unanimously to find Mr. Sussmann not guilty.

Some supporters of Mr. Trump had been bracing for that outcome. They pointed to the District of Columbia’s reputation as a heavily Democratic area and suggested that a jury might be politically biased against a Trump-era prosecutor trying to convict a defendant who was working for the Clinton campaign.

The judge had told the jurors that they were not to account for their political views when deciding the facts. The jury forewoman, who did not give her name, told reporters afterward that “politics were not a factor” and that she thought bringing the case had been unwise.

Mr. Durham expressed disappointment in the verdict but said he respected the decision by the jury, which deliberated for about six hours.

“I also want to recognize and thank the investigators and the prosecution team for their dedicated efforts in seeking truth and justice in this case,” he said in a statement.

Outside the courthouse, Mr. Sussmann read a brief statement to reporters, thanking the jury, his defense team and those who supported him during what had been a difficult year.

“I told the truth to the F.B.I., and the jury clearly recognized that with their unanimous verdict today,” he said, adding, “Despite being falsely accused, I am relieved that justice ultimately prevailed in this case.”

During the trial, the defense had argued that Mr. Sussmann brought the matter to the F.B.I. only when he thought The New York Times was on the verge of writing an article about the matter, so that the bureau would not be caught flat-footed.

Officials for the Clinton campaign testified that they had not told or authorized Mr. Sussmann to go to the F.B.I. Doing so was against their interests because they did not trust the bureau, and it could slow down the publication of any article, they said.

James Baker, as the F.B.I.’s general counsel in 2016, met with Mr. Sussmann that September. Mr. Baker testified that he had asked Eric Lichtblau, then a reporter at The Times working on the Alfa Bank matter, to slow down so the bureau could have time to investigate it.

Mr. Sussmann’s defense team offered the jurors many potential paths to acquittal, contending that the prosecution had yet to prove multiple necessary elements beyond a reasonable doubt.

His lawyers attacked as doubtful whether Mr. Sussmann actually uttered the words that he had no client at his meeting with the F.B.I. in September.

That issue was complicated after a text message came to light in which Mr. Sussmann, arranging for the meeting a day earlier, indicated that he was reaching out on his own. But it was what, if anything, he said at the meeting itself that was at issue.

Mr. Baker testified that he was “100 percent” certain that Mr. Sussmann repeated those words to his face. But defense lawyers pointed out that he had recalled the meeting differently on many other occasions.

The defense team also argued that Mr. Sussmann was in fact not there on behalf of any client, even though he had clients with an interest in the topic. And they questioned whether it mattered, since the F.B.I. knew he represented the Democratic National Committee and the Clinton campaign on other issues, and agents would have investigated the allegations regardless.

Midmorning, the jury asked to see a trial exhibit meant to bolster the defense’s argument that Mr. Sussmann did not consider himself to be representing the Clinton campaign. It was a record of taxi rides Mr. Sussmann expensed for the Sept. 19 meeting at F.B.I. headquarters.

He logged those rides to the firm rather than to the Clinton campaign or to the technology executive, Rodney Joffe, who had worked with the data scientists who developed the suspicions and brought them to Mr. Sussmann. Prosecutors asserted that Mr. Joffe was his other hidden client in the meeting.

During the trial, prosecutors had made much of how Mr. Sussmann logged extensive hours on the Alfa Bank matter to the Clinton campaign in law firm billing records — including phone calls and meetings with reporters and with his partner at the time, Marc Elias, the general counsel of the Clinton campaign.

Defense lawyers acknowledged that the Clinton campaign had been Mr. Sussmann’s client for the purpose of trying to persuade reporters to write about the matter, but argued that he was not working for anyone when he brought the same materials to the F.B.I.

In a statement, Sean Berkowitz and Michael Bosworth, two of Mr. Sussmann’s defense lawyers, criticized Mr. Durham for bringing the indictment.

“Michael Sussmann should never have been charged in the first place,” they said. “This is a case of extraordinary prosecutorial overreach. And we believe that today’s verdict sends an unmistakable message to anyone who cares to listen: Politics is no substitute for evidence, and politics has no place in our system of justice.”

WASHINGTON — President Biden said on Tuesday that the United States would send Ukraine advanced rocket systems and munitions that would enable it to more precisely target Russian military assets inside its borders.

In an Op-Ed published online Tuesday evening by The New York Times, Mr. Biden said the delivery of the advanced rocket systems would enable Ukraine to “fight on the battlefield and be in the strongest possible position at the negotiating table.”

Mr. Biden’s administration has already sent Ukraine billions of dollars worth of antitank and antiaircraft missiles, unmanned aerial vehicles, helicopters and other military equipment as the country seeks to repel Russia’s three-month-old invasion.

As the war has dragged on, the Biden administration has progressively widened the array of weaponry it has provided to the Ukrainians. But top administration officials have been concerned about provoking a broader war with President Vladimir V. Putin of Russia by providing weapons that could allow Ukraine to strike deep inside his country.

In his article, Mr. Biden stressed that the new rockets would be used to “strike key targets on the battlefield in Ukraine.” And he said the United States was not seeking to engage Russia in a broader conflict.

He stated bluntly that he did not seek to overthrow Mr. Putin, despite his off-the-cuff remarks during a speech in Poland earlier this year, when he said the Russian president “cannot remain in power.”

On Tuesday, Mr. Biden presented a different view.

“We do not seek a war between NATO and Russia,” he said. “As much as I disagree with Mr. Putin, and find his actions an outrage, the United States will not try to bring about his ouster in Moscow.”

He added: “So long as the United States or our allies are not attacked, we will not be directly engaged in this conflict, either by sending American troops to fight in Ukraine or by attacking Russian forces.”

Mr. Biden had told reporters on Monday that “we’re not going to send to Ukraine rocket systems that can strike into Russia.”

Officials have not supplied details on exactly which types of rockets the United States will provide. The one used most often by the Pentagon is the M31 GMLRS — for Guided Multiple Launch Rocket System — a satellite-guided precision weapon that carries roughly the same explosive power as a 500-pound bomb dropped from the air.

It can fly more than 40 miles, well beyond the range of any artillery Ukraine now uses. According to a report published by the Congressional Research Service in June, the Pentagon has spent approximately $5.4 billion to buy more than 42,000 such rockets since 1998.

But Mr. Biden made clear in his Op-Ed on Tuesday that the administration was ready to provide more advanced weapons to Ukraine as the Russian military makes gains in the eastern part of the country.

“Standing by Ukraine in its hour of need is not just the right thing to do,” he wrote. “It is in our vital national interests to ensure a peaceful and stable Europe and to make it clear that might does not make right.”

JERUSALEM — Government ministers from Israel and the United Arab Emirates signed a free-trade agreement on Tuesday that, once ratified, would be the widest-ranging deal of its kind between Israel and an Arab country and the latest example of deepening ties between the Jewish state and some Arab governments.

The text of the deal has yet to be published and is still subject to review by the Israeli Parliament and formal ratification by the Israeli government, a process that will take at least two weeks. But officials said that once confirmed, the agreement would loosen restrictions on almost all trade between the two countries and could increase its annual value 10-fold within five years.

The speed at which the deal took shape — it was sealed less than two years since the establishment of formal ties between Israel and the Emirates — highlights the readiness with which Israel is now being accepted by some Arab leaders after years of diplomatic isolation.

For decades, Israel was ostracized by all but two Arab countries, with the others mostly avoiding formal diplomatic relations with it because of the lack of resolution to the Israeli-Palestinian conflict.

That changed in 2020, when Israel, in four agreements brokered by the Trump administration, established diplomatic relations with Bahrain and the U.A.E., re-established them with Morocco and improved relations with Sudan.

The agreements reflected a shift in priorities by those countries, which now consider the creation of a Palestinian state of less immediate importance than building a united front against the threat of Iran and establishing better trade and military ties with Israel.

The trade deal signed Tuesday in Dubai by the Israeli and Emirati economy ministers — Orna Barbivay and Abdulla bin Touq al-Marri — is the most substantive consequence of those agreements.

The deal will lead to the removal of tariffs on 96 percent of goods traded between the two countries within five years, both ministries said.

Bilateral trade was worth $885 million in 2021, the Israeli economy ministry said. The free trade agreement may allow the annual value of trade to rise to $10 billion within five years, the Emirati economy ministry said.

The Israeli prime minister, Naftali Bennett, described the deal as “historic,” and said that the negotiations, which began around the time of Mr. Bennett’s visit to the Emirates last December, led to “the fastest F.T.A. to be signed in Israel’s history.”

Mohamed Al Khaja, the Emirati ambassador to Israel, called it “an unprecedented achievement.”

According to the Israeli government, the deal will enhance the trade of medicine, medical equipment, food, plastic goods and fertilizer, as well as Israeli jewelry.

The deal will also improve bilateral cooperation over intellectual property rights, copyright and patents, particularly in the technology and agriculture sectors. It could also help Israeli and Emirati companies compete for government contracts in either country, the Israeli statement said.

The deal follows several other milestones in the relationship between Israel and its new Arab partners.

Mr. Bennett and several of his ministers have met their counterparts in the U.A.E. and Bahrain — visits that were once considered unthinkable — and some ministers have also visited Morocco. Those warming ties have also bolstered Israel’s relationship with Egypt, its oldest Arab partner. Egypt and Israel sealed a peace deal in 1979 but avoided establishing a warm relationship until the recent thaw between Israel, the Emirates, Bahrain and Morocco.

In a sign of improving ties between Israel and Egypt, Mr. Bennett met in March in Egypt with both Mohammed bin Zayed, the Emirati leader, and the Egyptian president, Abdel Fattah el-Sisi — another summit that would have been hard to imagine before 2020.

Israel has also signed provisional defense agreements with the Bahraini and Moroccan defense ministries, making it easier for their armies to coordinate and trade military equipment. And in a highly symbolic meeting in March, the foreign ministers of Israel, Egypt, Bahrain, Morocco, the U.A.E. and the United States gathered in southern Israel, at the retirement home of Israel’s founding prime minister, David Ben-Gurion.

Jews living in the Emirates are also observing their religious traditions increasingly openly. Community leaders estimate that the number of resident observant Jews in Dubai has doubled, to 500, in the last year, and at least five kosher restaurants have opened in that time.

ALBANY, N.Y. — Money and lobbying hold enormous sway in the State Capitol, but there are few pressures like an old-fashioned deadline to get major legislation over the finish line.

With New York’s yearly legislative session scheduled to conclude June 2, state lawmakers are racing to put finishing touches on a wide range of legislative packages, from efforts to strengthen gun laws and reproductive rights to a deal to renew New York City’s authority over its schools.

The Legislature, controlled by Democrats, has already passed a steady stream of legislation in recent weeks, including a landmark bill to allow adult victims of sexual assault to sue their abusers, and legislation to ban the sale of cosmetics tested on animals. The Senate has passed bills to crack down on monopolies and cap the cost of insulin, though it remained unclear if the Assembly would follow suit.

Consensus on other hot-button legislation seemed even less certain, with many legislators already eyeing re-election campaigns and grappling with the chaos of new district lines that have led to a harried game of musical chairs.

Here’s a look at five of the most contentious issues facing lawmakers in their final week of session.

Raising the age to buy AR-15-style weapons

New York already has some of the strictest gun laws in the nation, but lawmakers want to further strengthen them, something they had been discussing even before the massacres in a Buffalo supermarket and a Texas elementary school.

The recent shootings, each involving 18-year-old suspects, only added momentum for new gun policies: Gov. Kathy Hochul, a Democrat, declared on Wednesday that she would seek legislation to raise the minimum age to 21 for the purchase of AR-15-style weapons, and perhaps other firearms.

Currently, anyone over 18 can purchase a long gun in New York as long as they pass a background check; permits to obtain a long gun are required in New York City, but not elsewhere in the state.

Raising the age for the purchase of at least some rifles, a step that other Democratic-led states have taken, appears to have support among Democratic lawmakers, even though it could be challenged in court by the gun lobby, which prevailed in California recently.

Lawmakers are discussing other gun-control measures, including a proposal to “microstamp” semiautomatic pistols to help law enforcement officials trace cartridge cases to the guns that discharged them.

State lawmakers are being cautious about the type of gun legislation they take on, wary of not passing any laws that the Supreme Court could use in its looming decision over the state’s concealed carry law, which many Democrats fear will be struck down. The law imposes limits on carrying guns outside the home.

“We don’t want to tip off any Supreme Court clerks who might be drafting an opinion and citing New York legislators trying to pre-empt their eventual opinion,” said State Senator Brad Hoylman, a Democrat who sponsored the microstamping legislation. “So there’s a lot of unease but also calculation that these bills don’t touch that area of concealed carry.”

Lawmakers may have some leeway in their timing: Ms. Hochul said this week she was prepared to call a special legislative session to pass bills in response to a Supreme Court decision, which is expected sometime in June.

Lawmakers weigh environmental impact of crypto mining

Two environmental bills are facing hurdles: One would impose a two-year moratorium on the most energy intensive cryptocurrency mining, while the other would task the New York Power Authority with building wind and solar plants with the goal of energizing the renewable energy market.

Proponents of both bills say they are critical to meeting goals of the Climate Leadership and Community Protection Act of 2019, a landmark law that mandated the state be 70 percent renewably powered by 2030, and carbon neutral by 2050. As of this week, New York received less than 3 percent of its power from wind and solar renewables.

“If the private sector is too slow to help us comply with C.L.C.P.A., which as of now it seems that we’re moving too slowly, we have a public entity that can help accelerate the pace,” State Senator Michael Gianaris, the Democratic deputy majority leader, said of the public utility bill, a top priority for progressives.

Opponents say that the bill is not necessary, given how many private-sector renewable projects are in the pipeline, and will lead to increased costs for consumers.

But it is the cryptocurrency bill — the first of its kind in the nation — which has received the most attention.

The bill would temporarily block new permits from being issued to facilities that are mining the digital currency using nonrenewable energy sources. The legislation is a direct response to the environmental concerns over old fossil-fuel power plants that have been converted into crypto mining facilities, especially for Bitcoin, across upstate New York.

The bill passed the Assembly in April, but the cryptocurrency industry — a newcomer in Albany politics — has mobilized to try to block the legislation in the Senate, where the chamber passed a broader moratorium last year.

The industry has argued that banning the operations would hurt the nascent industry in New York and open the floodgates for similar regulations by Congress and other statehouses. Ms. Hochul said this week that she was “open-minded” about the legislation, but wanted to balance the creation of upstate jobs with the environmental impact of the facilities, a concern echoed by other lawmakers.

“I think there is a way to make crypto mining fossil-free without using the stick, and instead using carrots to get there,” said State Senator Todd Kaminsky, a Democrat from Long Island.

New York City mayors have trekked up to Albany on a regular basis to renew the city’s control over its public schools ever since Mayor Michael R. Bloomberg first convinced lawmakers to grant him so-called mayoral control.

While local boards oversee schools in the rest of the state, lawmakers have typically granted the city authority over its schools in increments of anywhere from one to seven years.

Mayor Eric Adams, with the backing of the governor, has asked to extend mayoral control four more years, which is longer than any extension that his predecessor, Bill de Blasio, had received.

John C. Liu, who leads the State Senate’s New York City Education Committee, said he believed that four years was too long of an extension. He suggested that he would be open to a multiyear agreement, provided that certain issues like class size, and representation for English as a second language students, and those with disabilities, were addressed.

The broader question of school governance remains open, however, with Mr. Liu, a Queens Democrat, saying he believed the state should commission a study on how city schools had fared under two decades of mayoral control and how they compared to those in other large American cities.

Democratic lawmakers have been working on a package of bills that would strengthen New York’s already robust protections for abortion, following a leaked Supreme Court opinion indicating the court was poised to overturn Roe v. Wade.

Some of those efforts have been focused on shielding providers from liability for patients coming from states where abortion has been criminalized. Others seek to protect patients who travel to New York for sexual health care.

Democrats are also working to enshrine the right to an abortion in the State Constitution, a move Ms. Hochul has expressed support for. It remains unclear, however, whether lawmakers will advance language focused narrowly on abortion, or put forth a more ambitious bill, which would provide comprehensive protection from discrimination.

A real estate tax break about to expire

Democratic lawmakers appear poised to let expire a divisive tax incentive program that New York City developers have used for five decades in the construction of most large residential projects.

Both Ms. Hochul and Mr. Adams have pushed for the renewal of the much-debated subsidy, known as 421a, or a revamped version of the program, which is meant to help subsidize the construction of affordable housing.

But there has been little appetite to renew the program among progressive Democratic lawmakers who have cast the subsidy as a tax giveaway for developers in exchange for too few units of below-market rental apartments.

“If we’re going to have a program that grants such generous tax benefits, we need to make sure that the public benefit is commensurate with the tax revenue we’re foregoing,” said State Senator Brian Kavanagh, the chair of the housing committee. “I think we have an opportunity to do that in the future. It’s not something that needs to happen by next Thursday.”

The impact of the subsidy’s expiration on June 15 is not expected to be felt for years. Ms. Hochul said the state could revisit the program in the future, even as some lawmakers made last ditch attempts to assemble a package of housing bills that could include an extension of the program.

Lawmakers appeared to be nearing consensus on another housing front: legislation to help salvage New York City’s deteriorating public housing system, home to more than 400,000 low-income residents.

The legislation, which Mr. Adams has lobbied for, would create a Public Housing Preservation Trust aimed at unlocking federal funds to finance the repairs to thousands of public housing units suffering from leaks, heat outages and mold.