You have until April 18, 2023 to make IRA contributions for the 2022 tax year. For backdoor Roth, it will be a non deductible Trad IRA contribution and you will want to do the conversion right away. Let’s assume you are going to do the contribution and conversion in 2023 since it is now impossible to do it in 2022. As long as you have completed the rollover of your pre tax Traditional IRA money to your 401k by 12/31/2023, you are all set and will not owe additional taxes on your already taxed 2022 Traditional IRA contribution. That is why you (and I) are doing this type of rollover, to avoid pro rata taxes.

For your 2023 contribution, you have until the April 2024 deadline to make your 2023 contribution (and presumably the conversion, if you are going to do another backdoor Roth).

Edit: After rereading, my second paragraph made it seem like there is a deadline to do the Roth conversion. There is not. But if you allow money to sit in the Traditional IRA account instead of converting it to Roth, you will owe taxes on the earnings when you do the conversion.

As others have noted, as long as you do the backdoor Roth conversion step in 2023, the only IRA balance that matters is the one on 12/31/2023. Fun fact, if you want to, you can actually still do a backdoor Roth for tax year 2022. Then you have the rest of 2023 to decide to if you want to do it again for tax year 2023. I have just worked through this process for a similar circumstance for myself.