Do not enter the state refunds in TurboTax at all. You know they're not taxable, so there is no reason to enter them. Even if you enter them, no information about the refunds is going to be included in your tax return, since they are not taxable.
The TurboTax interview doesn't handle refunds for multiple years very well. You might have misunderstood a question or answered a question incorrectly, or the question might have been poorly worded. In your situation, the best approach is to not enter the refunds at all.
Whether you use the standard deduction or itemized deductions on your 2022 tax return has no effect on whether the state refunds are taxable.
