if you intend to return to NJ after 2021, NJ would deem your domicile and thus the state to pay income taxes to be NJ for 2021.
from NJ individual income tax instructions
Domicile. A domicile is the place you
consider your permanent home—the
place where you intend to return after a
period of absence (e.g., vacation, business assignment, educational leave). You
have only one domicile, although you
may have more than one place to live.
Your domicile does not change until you
move to a new location with the intent to
establish your permanent home there and
to abandon your New Jersey domicile.
Moving to a new location, even for a long
time, does not change your domicile if
you intend to return to New Jersey.
as for federal MFS vs MFJ you usually will pay more federal taxes than if you use another filing status for which you qualify. Also, if you file a separate return, you can't take the student loan interest deduction, the tuition
and fees deduction, the education credits, or the earned income credit. You also can't take the standard deduction if your spouse itemizes deductions.
