DaveF1006 is incorrect. Because the distribution occurred in 2022, depositing the money within 60 days into a Roth IRA as a Roth conversion would be reportable on your 2022 tax return as a Roth conversion. There is no requirement that the deposit into the Roth IRA be completed before the end of the year. (The reference to DavidD66's post does not apply. That post was in response to a question asking if a distribution performed in 2021 could be reported as income on a 2020 tax return.)
The only oddity is that the conversion deposit will appear on the Roth IRA's 2023 Form 5498 rather than a 2022 Form 5498 despite this being a 2022 Roth conversion. This is not a problem. The IRS is well aware that indirect Roth conversions might be completed early in the year following the year of the distribution.
Assuming that you complete the Roth conversion, when entering the Form 1099-R that reports the distribution you'll indicate that you moved the money to another retirement account, that you did a combination of rolling over, converting and cashing out, then indicate the amount converted.
