When Mayor Eric Adams unveiled the final budget of his first (and possibly last) term in office on Thursday, there was no sign of proposed cuts to libraries in the $114.5 billion document, as there had been in years past.

There were no warnings that the surge of undocumented migrants to New York City would prompt budget cuts. There were no new big-ticket initiatives, as one might expect in an election year, with the mayor facing a battalion of well-funded challengers and a federal corruption trial that is set to begin just weeks before the Democratic primary in June.

Instead, the mayor offered a more optimistic budget blueprint, one filled with increasing revenues buoyed by surging business taxes and lower spending for a migrant influx that has slowed in recent months.

“I think it’s really underrated how well of a fiscal manager I have been for the city,” Mr. Adams said on Thursday. “We turned the city around,” he added.

During his budget address, Mr. Adams said his administration had “set the table for success” by managing expenses and spending strategically.

The mayor’s budget projects spending some $2 billion less for asylum seeker services than originally projected through the 2026 fiscal year, an apparent byproduct of the outgoing Biden administration’s border restrictions and the city’s own efforts to pressure migrants to leave the shelter system.

The city says it has seen 28 straight weeks of declines in its census of asylum seekers.

The reduced spending projections on migrants also seem to acknowledge that the administration had been overstating its projected costs, as the city’s independent budget watchdog contended this month.

“Perhaps the biggest gimmick here is that $2.4 billion of the $2.7 billion that the mayor is claiming in savings is merely correcting for his past overbudgeting of asylum seeker costs, which the Independent Budget Office has highlighted,” Brad Lander, the New York City comptroller, said in a statement. Mr. Lander is running for mayor.

But the city also projects spending $550 million more this fiscal year on homeless shelter services unrelated to asylum seekers, and another $325 million on rental assistance, as the city’s conventional homeless population surges.

On Thursday, the mayor attributed the rising homeless population to people migrating to New York City’s shelters from elsewhere in the United States.

Mr. Adams said there was “a substantial number of people” from outside New York coming to the city but that he wasn’t sure why.

The city projects budget gaps of $4.2 billion in the 2027 fiscal year and $5.4 billion in the 2028 fiscal year. The city is planning to put no additional money into reserves, even as the nonpartisan Citizens Budget Commission argues that the city is understating those upcoming budget gaps.

“The city chose not to take this opportunity to add to its reserves but should do so if revenues continue to exceed projections or spending is lower than expected,” Thomas DiNapoli, the New York State comptroller, said in a statement. “With the potential for significant policy changes at the federal level in the coming year that could affect city finances, this should be imperative.”

This proposed budget is Mr. Adams’s fourth, and the last before he mounts what appears to be an uphill bid to retain the mayoralty. Mr. Adams is facing trial on five federal corruption counts in April. His legal defense fund is in the red.

The budget funds several relatively modest initiatives that the mayor announced in his State of the City address this month, including increasing homeless shelter capacity and building up to 100 beds with temporary, wraparound services for mentally ill patients who are transitioning out of hospital care and have no homes to go to.

The mayor’s budget proposal is negotiated with the City Council, and by June 30, it must pass a budget for the fiscal year beginning July 1.

“The investments in this plan simply do not meet the moment or match the scale of the needs of the city,” said Justin Brannan, the chair of the City Council’s Finance Committee. “New Yorkers are struggling, especially working families. They need the city to help them, help with the outrageous cost of child care and early childhood education, help by investing in an affordable CUNY, help them unwind in a safe, clean park and we’re not seeing any of that in this plan.”