How constrained is the NYC mayor?

I thought to ask o3, here is the opening of its answer:

New York City has a “strong-mayor / council” system, but the City Charter, state law and an array of watchdog institutions deliberately fragment power. In practice the mayor can move fastest on implementation—issuing executive orders, running the uniformed services, writing the first draft of the budget, and appointing most agency heads—yet almost every strategic decision runs into at least one institutional trip-wire.

He does appoint all police commissioners and has direct control over the police.  The mayor also has line item veto authority, although that can be overriden by the City Council.  The entire response is of interest.  More generally, who will and will not feel welcome in the city after this result?