No. Wages you earned in New York in 2021 but paid out in 2022 are still New York source income, as would payouts for accrued sick time and vacation upon leaving a company.
New York says NY source income includes:
any income you received related to a business, trade, profession, or occupation previously carried on in New York State ....
See Tax Bulletin IT-615 (TB-IT-615)
File a non-resident New York return to report your income.
The same income is also taxable by New Jersey because you were an NJ resident when you received it.
You can claim a credit on your NJ return for tax paid to NY.