Your spouse's 2023 state refund is not taxable and does not have to be reported, because your spouse did not itemize deductions on his/her 2023 federal tax return. When reporting your state refund, ignore your spouse's refund and answer all the questions about the state refund as if they apply only to you. On the screen where you enter your state refund, enter only your own refund (even though it says "Total Refund Received"). A couple of screens later it asks whether you took the standard deduction or itemized in 2023. Select "I itemized my deductions in 2023." One or two screens later it offers two choices. You can use either one. You can take the easy way out and just make the full amount of your refund taxable. Or you can select the option to enter information from your 2023 tax return. If you do that, enter the information from only your own 2023 tax return.
(Note to anyone else reading this: This solution only works because the spouse took the standard deduction in 2023.)