There is no question that the Roth conversion must be reported on the the 2022 tax return because the income resulting from the distribution from the traditional IRA was received in 2022. The same would be true of a rollover of a traditional IRA distribution and a conversion is defined as a special type of rollover. Although it's in reference to a distribution which is taxable due to not being rolled over, the same applies to Roth conversions where IRS Pub 590-A states: "These amounts are taxable in the year distributed, even if the 60-day period expires in the next year." This is how it has always worked since the inception of IRAs in 1975.
What is less apparent is the effect on the two 5-year rules. However, these are well addressed in the Roth IRA statute and regulations, in particular 26 USC § 408A(d)(3)(F)(i)(II) and 26 CFR § 1.408A-6 Q&A-2. Note that there are always two parts to a Roth conversion: a distribution from the traditional IRA and a "conversion contribution" (a particular type of rollover) to the Roth IRA. In this case, the conversion contribution occurs in 2023 and will be reported on a 2023 Form 5498 and is what the IRS looks to to determine the beginning of the 5-year periods.
