This is what is supposed to happen.
First, you enter the IRA contribution in the IRA section on the deductions and credits page. You may be told that you can't deduct it, or you may be asked if you want to take a deduction, in which case you say "no."
Then, enter the 1099-R showing the full withdrawal. Turbotax asks what you did with the money and you say you converted it to a Roth IRA.
Both of these facts go on form 8606. You should have a form 8606 as part of your 2023 tax return that has the following information:
Line 1 (current non-deductible contributions) $6500
Line 2 (prior non-deductible basis) $0
Line 8 (conversions) $19,500
Line 11 (non-taxable conversion) $6500
Line 15c (taxable amount) $13,000.
If line 1 does not show your current (2023) non-deductible contribution, then you entered it wrong or didn't enter it in Turbotax. You can amend your return to change your answers, and report the non-deductible contribution. If line 1 does show $6500, and line 15c shows $13,000, then you paid the correct tax on the conversion.
