Your understanding is correct. If the distribution from the traditional IRA occurred in 2022, you'll have a 2022 Form 1099-R that is reportable as a conversion on your 2022 tax return.
There are two only effects that completing this conversion in 2023 instead of in 2022 would have. The first is that the 5-year conversion clock will start on January 1, 2023 instead of January 1, 2022. possibly delaying by one year penalty-free access to the converted funds. Similarly, if this established your first Roth IRA, the date on which the 5-year clock for qualifying your Roth IRAs will start on January 1, 2023 instead of January 1, 2022, possibly delaying by one year tax-free excess to earnings.
