I ran your scenario through TurboTax and discovered that New Jersey is going to pick up all the federal income and treat it as income taxable in New Jersey. So, New Jersey will pick up the bulk of your wages, accept for items that are excluded from federal wages, such as 125 medical insurance benefits and FSA contributions. These items must be included in your New Jersey income, so you will have to enter those things separately.
There is a screen in your New Jersey program that references "other wage adjustments - W-2" where you can add the income items that are taxable in New Jersey but not included in wages as reported on your W-2 form, in box 1. You may see these items referenced in box 14 on your W-2 form. I suggest you look at your W-2 form from 2019 and see what was added to your New Jersey state wages in box 16 as a guide to what you should add in 2020.
It would pose a problem on your New York return if you worked in New Jersey and New York, but it sounds like that is not the case. It seems that you just work in New York, and if so all of your income would be taxable to New York.
So, it seems you can enter the W-2's and the adjustments mentioned and then complete the credit for taxes paid to another state on your New Jersey return and your tax in both states should be properly stated.
[Edited 4/7/21 12:18 PM PST]
@PJackson
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