Yes, you should claim the state tax refund as income on your 2024 tax year return.
Yes, the questions the program asks is in regard to how you filed your 1040 for tax year 2023. Since you filed Form 1040NR, those questions are not relevant.
This IRS link reports that a refund of state tax that would have increased the previous year tax liability is reported as income for the year received. This is the case for your situation.
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