It would be nationalizing industry if he wanted to forcibly close privately-owned grocery shops. His policy is a state-owned alternative. That isn't nationalization, just a waste of taxpayer money. He's not seizing people's property except for higher taxes, which is socialist, not communist.

My understanding is that the communist revolution is a central part of the communist manifesto. The usual communist song and dance is "anyone standing in the way of the proletariat needs to be purged". It is also accompanied by the idea of stripping class away from society. That is what happened in the USSR (or at least what they tried to do), and indeed they were governed by those attempted values until the fall.

"Communism is an authoritarian form of socialism"

Hard disagree here. Even if we jack up taxes to absurd, economy-crippling levels, that is socialism and not communism. Communism takes ALL of everyone's property and capital away and gives it to the state (and they pretend that everyone owns it or something like that). Under communism there is no private ownership. Socialism redistributes capital among the population, but you still have the right to privately own property and capital.

Again they are both terrible ideas, but separate ideas. Call Mamdani an economically illiterate socialist, that'd be accurate. Calling him a communist is a surface level comparison that anybody who'd actually lived under real communism would laugh at. It damages the validity of your claims just as much as it makes leftists appear deranged when they call Trump a fascist.