You should file an NC return on which your wife declares zero NC income, but reports her NC withholding. This should result in a complete refund of her NC tax withholding.
You can file the return MFJ. You'll have to put both your incomes on the return, but you won't be taxed.
You could file the NC return MFS, but North Carolina makes you jump through some hoops if you file federal MFJ and NC MFS. From page 12 of the 2021 NC filing instruction booklet:
"If you file a joint federal return and your spouse is a nonresident of North Carolina who had no North Carolina taxable income, you may file a joint N.C. tax return or a married filing separately N.C. tax return. If you choose to file a separate N.C. return, you must complete either a federal return as married filing separately reporting only your income and deductions or a schedule showing the computation of your separate income and deductions and attach it to your N.C. tax return."
https://www.ncdor.gov/media/13143/open
If NC questions the return, explain to them that your wife is an SC resident who never sets foot in NC for her work.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
