“His primary tool for governing is to create fear,” said Karen Hinton, a communications consultant who worked with Mr. Cuomo when he was housing secretary in the Clinton administration and has since fallen out with him.

In the fall of 2018, for example, when Mr. Cuomo was told by a leader of the Working Families Party — which had backed his primary opponent, Cynthia Nixon — that it would endorse him in the general election because he was better than a Republican, Mr. Cuomo’s response was blunt.

“If you ever say, ‘Well he’s better than a Republican’ again, then I’m going to say, ‘You’re better than a child rapist,’” the governor said, according to two people who were on the call. “How about that?”

He once threatened to end the career of a staffer who failed to properly transfer a call to his office, according to one person who worked for him and requested anonymity for fear of retribution. He has been known to refer to his top female aides as the “mean girls,” said the person, who described the governor’s office as toxic and controlling.

Those who work in the halls of the Capitol say the governor’s conduct has an additional impact: scaring some employees into near paralysis for fear of earning his wrath.

Many of the tactics involve a threat to hurt people’s careers. Ms. Hinton, for example, says she fell out of favor when she became the press secretary for Mr. Cuomo’s nemesis in the Democratic Party, Mayor Bill de Blasio.

Soon, there were threats. During a Legionnaires’ disease outbreak in 2015, Ms. Hinton questioned the state’s response in a New York Times article. Ms. Hinton said Mr. Cuomo told City Hall he would personally blame the mayor for any deaths in the city if Mr. de Blasio did not fire Ms. Hinton. The mayor did not dismiss Ms. Hinton, but City Hall distanced itself from her remarks.

One current and one former City Hall official confirmed Ms. Hinton’s account. The governor’s office said neither it or the anecdote about the Working Families Party was true, characterizing the negative comments about Mr. Cuomo, a third-term Democrat, as coming from “political adversaries.” The office also said the governor was “direct with people if their work is subpar.”

“The people of this state have known and given the governor their trust for the last 14 years, have heard him and looked into his eyes during the darkest period,” Richard Azzopardi, a senior adviser to Mr. Cuomo, said in a statement. “Yes, they have seen him get impatient with partisan politics and disingenuous attacks, and New Yorkers feel the same way. They know you must fight to change the status quo and special interests to make progress, and no one has made more progress than this governor.”

Even Mr. Cuomo’s detractors will concede that the governor’s heavy-handed approach has often been effective in delivering concrete liberal accomplishments, including legalizing same-sex marriage, raising the minimum wage and enacting criminal justice reforms.

Mr. Cuomo’s image was burnished by a series of nationally televised news conferences during the early days of the pandemic, in which the governor mixed just-the-facts presentations with dad jokes and appearances by his three daughters, his mother and his brother, Chris Cuomo, the CNN anchor. Last fall, even as a second wave of the virus began to swell in New York and nationally, he published a memoir, offering “leadership lessons” and a sentimental dedication.

“Love wins,” he wrote in its conclusion. “Always.”

But in the wake of the scandal over nursing homes, that persona has turned darker: On Saturday, Mr. Cuomo’s temper was mocked in a segment on “Saturday Night Live” in which his character, played by comedian Pete Davidson, sheepishly admitted to hiding where the deaths of nursing home residents occurred and promised vengeance on Mr. de Blasio, a frequent political foe.

Other accusations have been more serious: In December, a former top aide to Mr. Cuomo’s economic development agency, Lindsey Boylan, accused Mr. Cuomo of fostering a “toxic team environment.

On Sunday, Ms. Boylan was among a growing chorus of people speaking out about Mr. Cuomo, telling The Times he is prone to “screaming at people inside and outside of the state government when he does not get exactly what he wants.”

Mr. Cuomo’s penchant for tough-talk tactics dates back decades, to his apprenticeship as an adviser to his father, former Gov. Mario M. Cuomo, whom he was known to fiercely defend. “I think he learned it from his father, who needed bare knuckles to combat the old machine pols,” said Michael Shnayerson, author of “The Contender,” a 2015 biography of the younger Mr. Cuomo.

State Senator Liz Krueger, a Democrat from Upper Manhattan who holds sway in the Legislature as the chairwoman of the chamber’s finance committee, said she had never been yelled at by the governor or his staff — for a reason.