Historically, a socialist holding an elected executive position of a capitalist government is a precarious position fraught with contradictions. You can only meaningfully govern by making massive concessions to the ruling class and betraying some supporters. Communists will stake out the “he will betray you” position.

FWIW the Mamdani administration is very aware of this contradiction and deliberately made promises that he can do by decree, such as the rent freeze. But there’s also been some rather heinous concessions, like keeping on a bunch of Zionists in the admin, and also keeping on the NYPD commissioner Jessica Tisch.