If Cuomo runs independent, the democratic party loses any hope of keeping their progressive base and it might actually split entirely.
After bullying their base for the last 10 years to get in line behind their shit moderate candidates, if they were to suddenly decide that primaries don't mean anything then they'd never be able to convince progressives to vote against their interests again.
Cuomo is backed by the democratic establishment and the DNC's donor class. It doesnt matter if he's independent, he's the establishment pick and would be running with their funding.
Mamdani's proposal is to raise taxes on any company doing business in NYC. They wouldn't be able to just change residency, they'd have to stop doing business in New York entirely.