If Mayor Eric Adams needed any further evidence of his diminished stature in New York City, this past week was a new low point.

On Tuesday, the mayor’s handpicked choice to become the city’s top lawyer withdrew his nomination, sparing himself and the mayor from a public rejection.

Two days later, a separate embarrassment emerged: Mr. Adams’s police commissioner, Edward A. Caban, resigned under duress. Mr. Caban and his twin brother are under federal investigation, one of four federal inquiries circling the highest levels of the Adams administration.

The swarm of federal scrutiny has raised questions about Mr. Adams’s fitness to lead the city; his ability to negotiate with the City Council and with state and federal leaders to push his agenda; and his capacity to lure and retain talented people in city government.

The scrutiny has also made his path to re-election more unwieldy. On Friday, a fourth prominent Democrat, State Senator Jessica Ramos, joined a crowded field of mayoral hopefuls seeking to stop Mr. Adams from winning a second term.