Most states take the attitude, in that situation, that the income was earned in NY and is subject to NY tax. As such, they usually require your employer to withhold NY tax, when they pay the bonus to you.
So, as, a practical matter, if your employer withheld NY tax, on the bonus, you're stuck with having to file a NY return for 2021. NJ will also tax it (because it was received while you were a NJ resident) but will give you a credit for what you paid NY. There will be little or no double taxation, but you have the hassle , and cost, of filing two state returns.
