No, you don't need to include the 2023 Form 1099-R with code P on your 2023 tax return if you did not have any tax withholdings in box 4 and 14. If you had tax withholdings then you must enter the 2023 Form 1099-R into the 2023 tax return since the withholdings are reported in the year that the tax was withheld. TurboTax will ignore the income because of the code P but the withholdings will be applied to 2023.
If you did not add the excess deferral to your wages on your 2022 return when you filed your 2022 return then you will need to amend the 2022 return.
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