As long as the pandemic is the reason that you are working from home you are okay. New Jersey has announced that they will accept New York's position that it is New York source income. So as SteamTrain said, you file the same way you have in the past, the same as if you were actually working in New York. And you continue to have New York tax withheld. So at least for 2020 you have no problem.
Where you might have a problem later on is when the pandemic is no longer a factor and you are working from home for your own convenience. New Jersey's policy of accepting it as New York income is only temporary, specifically for the pandemic. You asked "Would it then be legally considered NY income?" The problem is that New York and New Jersey have conflicting laws. According to New York law it is legally New York income. According to New Jersey law it is legally New Jersey income. Where this makes a difference is in being able to claim the Credit For Income Taxes Paid to Other Jurisdictions on your New Jersey tax return. One of New Jersey's requirements for the credit is that "The income must have been properly taxed by the other jurisdiction." But since the income is for work performed in New Jersey, they do not consider it properly taxed by New York. That would mean that you can't claim the credit, so you would have to pay both full New York tax and full New Jersey tax on the same income. I don't have a good answer for a legal way to handle this.
Working from home for your own convenience will also cause a problem for your employer if they do not already have any presence in New Jersey. Having you working in New Jersey, regardless of whose convenience it's for, would make them a New Jersey employer. They would not only have to withhold New Jersey tax from your pay, but they would also be subject to New Jersey tax on part of the company's income. Because of this, they probably would not allow you to do it. You might not be happy about that, but it would eliminate your double taxation problem. On the other hand, if the company does already have a presence in New Jersey, they could probably assign you to their New Jersey location. Then you would no longer be a New York employee. You would be a New Jersey employee, they would withhold New Jersey tax, and not New York tax, and all the problems would be eliminated.
From what I can see, there is essentially no chance that New York will change their position on telecommuting unless they are forced to by the courts or by a federal law that overrides the state law. Neither of those appear to be on the horizon.
