Feud? What Feud? Hochul’s New York City Visit Suggests a Peace Offering.

Kathy Hochul, New York’s lieutenant governor, savored deep-fried cookie dough at the Erie County Fair and toured a public school in Queens. She went on the morning news shows on Sunday, met with a few of the outgoing governor’s political enemies on Tuesday, and is planning a fund-raiser in Buffalo on Wednesday.

And in Albany, Andrew M. Cuomo, the soon-to-be ex-governor, filed his retirement papers.

Ms. Hochul has kept a busy schedule in her first week as New York’s governor-in-waiting, basking in the limelight as she juggles national media attention and a government transition after Mr. Cuomo announced he would resign next week.

Ms. Hochul, who takes office on Tuesday, has used the intervening period to introduce herself to most New Yorkers after nearly seven years of being sidelined in a mostly ceremonial role in the Cuomo administration. A Democrat from the Buffalo area, Ms. Hochul made a point of visiting New York City this week, seemingly intent on mending the deeply fractured relationship between Albany and City Hall, saying that she was bringing “a different approach to governing.”

“I’m excited about this,” Ms. Hochul said on Wednesday after touring a school in Corona, Queens, with a group of elected officials. “I’m excited about this opportunity and, I’d like to reiterate, I’m very prepared for this.”

Mr. Cuomo, for his part, has kept a relatively low profile since he announced his resignation last week following a New York State attorney general report that found he sexually harassed multiple women, including government employees, and fostered a toxic workplace.

Mr. Cuomo and Ms. Hochul have not spoken since last Tuesday, when he promised her a smooth transition during a phone call. When the governor issued a major directive on Monday mandating that all health care workers receive at least one dose of the coronavirus vaccine by the end of next month, an accompanying news release noted that Ms. Hochul’s team “was briefed prior to the announcement.”

One thing Mr. Cuomo had not done as of Wednesday afternoon was submit his formal resignation letter to the New York Department of State, a requisite ahead of his departure, fueling speculation among his longtime critics about his intentions. His office declined to comment on the matter.

But in a sign that the governor’s third term is in fact coming to an end, Mr. Cuomo, 63, filed for retirement with the state comptroller’s office on Tuesday, a requirement that will entitle him to an estimated pension of at least $50,000 a year following his more than 14 years of service, including four years as state attorney general.

The governor also commuted the sentences of five people and fully pardoned five others on Tuesday. He may act on bills sitting on his desk in the coming days.

Hochul officials confirmed that Mr. Cuomo’s time in office will end at 11:59 p.m. Monday. Ms. Hochul will be sworn in immediately after.

Ms. Hochul met on Tuesday with Mayor Bill de Blasio, who has had an infamously toxic relationship with Mr. Cuomo, to discuss the coronavirus Delta variant, health precautions at schools and public safety. Ms. Hochul posted a picture of the meeting on Twitter that shows the two of them laughing over pastries — a starkly different image than any representing the mayor’s relationship with Mr. Cuomo.

Before the meeting, Mr. de Blasio, a Democrat in his last year in office, said he had a good relationship with Ms. Hochul and, as he has in the past few months, did little to hide his contempt for Mr. Cuomo, saying the outgoing governor “was really aberrant.” After the hourlong meeting, Mr. de Blasio said, “It was just a good, healthy, sane — emphasize the word sane — conversation, which I totally appreciated.”

Ms. Hochul also met with Jumaane Williams, the city’s public advocate and a vocal critic of Mr. Cuomo. Her meeting with Mr. Williams drew interest because the two were once political rivals: Mr. Williams ran unsuccessfully for lieutenant governor in 2018, mounting a surprisingly strong bid, but losing to Ms. Hochul by about 7 percentage points.

Losing no time, Ms. Hochul said over the weekend that she would run for governor in 2022, giving her a head start and the advantage of incumbency in what is expected to be a contested field. Mr. Williams, a progressive who is to the left of Ms. Hochul, has not ruled out a run for governor next year.

In a joint statement issued after the meeting, Ms. Hochul and Mr. Williams said they had discussed gun violence, and how to fix state-run programs that have been slow to deliver relief to tenants and landlords, as well as cash payments to undocumented immigrants who were not eligible for federal aid.

Ms. Hochul has also begun previewing her administration’s response to the coronavirus, saying on Wednesday that she anticipates announcing a statewide mask mandate in schools when classes begin next month.

But as she prepares to take office, Ms. Hochul must contend not only with thorny policy issues, but personnel moves, too. She faces difficult decisions over which Cuomo officials she will retain and which she will oust as she seeks to distance herself from the scandals that enveloped the outgoing administration.

On Wednesday, she seemed to suggest there would not be an immediate overhaul of Mr. Cuomo’s cabinet, saying that she would take up to 45 days to make those decisions. She said she was still in the process of “getting people’s opinions and putting together the ‘dream team’ to run the State of New York into the future.”

She has chosen a seasoned Albany strategist as the director of her transition team: Marissa Shorenstein, who was press secretary under Gov. David A. Paterson and the director of communications for Mr. Cuomo’s campaign in 2010, before leaving for the private sector.

Ms. Hochul has also begun laying the groundwork for her election campaign, saying on Sunday that she would soon pick a lieutenant governor from New York City, an attempt to balance her ticket.

She has hired political consultants with experience on national campaigns, formally filed to run for governor and raked in more than $60,000 in campaign contributions since the release of the state attorney general report. Contributions began to pour in from at least one union previously aligned with Mr. Cuomo, as well as from well-connected donors from Buffalo.

On Wednesday evening, Ms. Hochul is holding a fund-raiser in Buffalo — billed as a celebration for her 63rd birthday — that had to be moved to a larger location because of a spike in interest. Admission prices range from $50 to more than $1,000 per guest.

Jeffery C. Mays contributed reporting.