The trustee of the account does not know if you deducted the contribution or not. The code P on the 2023 Form 1099-R indicates that the amount needs to be reflected in the way that you filed the 2022 tax return, in this case by not deducting the contribution. If the IRS questions your 2022 tax return, you'll just need to provide an explanation as you did in your post above.
As you said, report the only the code-8 2023 Form 1099-R on your 2023 tax return. (I assume that the code-P Form 1099-R shows no tax withholding.)
