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@Tiborone 

If you want the contribution to be recorded for 2022, you must report the nondeductible IRA contribution on your 2022 tax return using form 8606.  And if your spouse also made a 2022 nondeductible contribution, they must have a separate form 8606 in their name as part of your tax return.

Then, you may do the Roth conversion at any time that is convenient for you. The Roth conversion is always reported on the tax return for the day that it happens. Even if you did the conversion on January 2, it must be reported for 2023, because conversions are never retroactive. 

The conversion is not tied in any way to the date of the contribution, it can happen anytime. In fact, if you are planning to make another $6000 nondeductible contribution for 2023, you could make that contribution now and then convert the $12,000 all at once. you don’t have to do it in $6000 increments. 

And yes, if you did the conversion now and you have $109 of earnings, the earnings will be taxable as of the date of the conversion.  (The only reason to try and make the conversion happen soon after the contribution is to minimize the conversion of taxable earnings, but it is not required that you do this as long as you pay the tax.)