Too many extensive "IF's" and What-If's" with all of that.
BUT
From what you describe, and unless NY issues some significant telecommuter tax adjustments due to COVID working issues, you would still be subject to the NY telecommuter tax, and nothing would change from what you've done in prior years. The NY company could still be required to withhold NY taxes, you would file a NY nonresident tax return for the year's wages at the NY company, and a NJ tax return for ALL your income from everywhere for the year, and take a NJ credit for the taxes paid to NY.
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Working from home (WFH) again for 2021...probably the same thing. Again, Unless NY changes their telecommuting rules some, due to COVID forcing people to work from home in a state other than NY.
But there are a couple recent articles about NY not changing their stance for 2020 taxes, even if telecommuting due to COVID:
https://www.natlawreview.com/article/new-york-issues-tax-guidance-covid-19-telecommuters
https://www.twrblog.com/2020/10/bad-news-for-new-york-nonresident-telecommuters-new-york-issues-covi...
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm#telecommuting
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Potential Complications: Things might change though in other states .....some states (as I recall, notably CA, MA and SC have issued some new guidance about taxation and telecommuting, and other states may also be considering telecommuter tax changes), Thus other states may be reviewing their tax laws about telecommuting and where and how state taxes may be required, due to the WFH issue and whether the employee working from home in that state, or a different state is a "convenience", or may now be a "requirement" due to COVID reasons. Navigating those issues may become a problem, but but too soon to know yet.
BUT again, as noted in the reference articles, for NY, things don't seem to be changing.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
