Since the $3,600 of state tax deduction reduces your federal taxes, that is the amount that would be taxable in 2024, assuming the refund was not reduced to $0. In other words, you need to know how much state tax was used to reduce your taxes in 2023. If you had a refund of more than $828 in this case before you entered the $3,600 of state tax deduction, then all of the state tax was used to reduce your tax in 2023, so it would all be taxable in 2024. So your taxable income in 2024 would be $3,600, the amount you deducted from income in 2023.
When you file the 2023 tax return you could take the standard deduction and that would eliminate the state tax refund issue in 2024. You could also reduce your state tax deduction by $3,600 and still itemize. Then your state refund would not be taxable in 2024, since you didn't deduct it in 2023. I don't know of any other way around filing the estate tax return in 2024, as the refund will make the income over $600.
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