Something doesn't sound right. If you did the conversion on 1/3/23, why did you get a 1099-R for 2022? I'm thinking the conversion/distribution would go on your 2023 tax return, but the contribution would go on 2022's, so you'll have a basis of $6,000, and a Trad IRA balance of $6,317 as of 12/31/2022 when you do your taxes next year. But if you got a 1099-R for 2022 then it seems like something else is off.
