No, not at all. Socialism is a reaction to extreme capitalism, and basically a call for socialism today is just saying "capitalism is cool and all, but there needs to be some guardrails so capitalism doesn't eat itself".

People voted for the mayor in NYC because capitalism started to eat itself in NYC, and the non-billionaires who actually make up the vast majority of the city wanted a change.

A simple, and reasonably small increase in taxes on the wealthiest of the wealthiest (who are in NYC because its a world class city and their businesses couldn't really "make it" as easily elsewhere) is not socialism. It's saying to the hedge fund billionaires "hey - we don't appreiciate that you're operating your businesses here yet refusing to help pitch in financially in order to keep our world-class city world-class". If Ken Griffin can afford to drop a quarter billion dollars on an apartment he spends ~25 days a year in, or Bill Ackman wants to continue to hire people educated at Colombia and NYU, they can afford to pay another 2-5 million dollars a year in tax".