That is google. They don't have to withhold that. IF google didn't withhold that state tax -- it would be impossible for NY to figure out how much it is owed. You can ask google to not withhold for NY with a HR meeting.
The issue with the current situation is that in principle I could be doing the work in New York (it doesn’t matter where I do it), but the office is closed and I don’t live in New York. So I have strong reasons for not doing my work in New York, but in principle I could be doing it there.
I guess there’s a further clause that you have to spend at least one day out of the year in New York to be taxed there, which unfortunately I have done (despite no longer traveling there for any work-related purpose).
It’s unclear at this point whether New Jersey will let New York claim all this taxable income or whether New Jersey will try to claim it for itself (it needs the money too). The tax rates are pretty similar in both states but my preference would be for the money to go to the state I actually live in.
And NY will demand their taxes 100%.