Not yet. Even though you made the non-deductible contribution to the Traditional IRA for 2021, the actual conversion to the Roth IRA took place in 2022. You will receive a 2022 Form 1099-R reporting the conversion, which will then be reported on your 2022 tax return.
As for the Form 1099-R with code J8, you are correct about what it is reporting.
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