Yes, the 2023 Form 1099-R should have code P and J for the removal of a 2022 excess contribution removed in 2023 according the the Form 1099-R Instructions.
If your financial institution refuses to correct the code I would document that they refuse to use the correct codes according to the Form 1099-R instructions and keep it for your records.
Like mentioned above you had no taxable earnings and therefore nothings is entered as taxable in box 2a and therefore you do not need to amend your 2022 tax return to add the 2023 Form 1099-R with code P (which should be P and J).
You also do not need to add it on your 2023 tax return because code P tells TurboTax it belongs on the 2022 tax return.
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