Yes, if you transferred your 2022 return into 2023, TurboTax should fill in the amount of State Tax Refund from last year for you.
The 'Total of of Tax Payments and Withholding' amount applies to 2023 and will also be filled in for you, after entering all your W-2's and 1099's that have withholding.
You generally have no need to enter any Other Taxes Paid, unless they are not included on any document you entered.
Here's more info on State Tax Refunds.
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