Should we just add/subtract the numbers from both last year returns and write the result in TurboTax when asked about state refund?
You do not combine the refund that one of you received and the amount that the other one owed. Answer all of the questions in TurboTax about the state refund using only the refund that one of you received. When it asks for information from your 2022 tax return, enter the information only from the 2022 tax return of the one who got the refund. You don't do anything with the amount that the other one owed. It does not affect the treatment of the refund.
Did the one who got a state refund for 2022 itemize deductions on his or her 2022 federal tax return, and claim an itemized deduction for state income tax on Schedule A line 5a? If not, or if the person who got the state refund used the standard deduction on Form 1040 line 12 of his or her 2022 federal tax return, then you can just ignore the state refund. Don't even enter it in your 2023 tax return.