I concur with others who say you should pay the taxes owed in the quarter that you did the conversion. I am doing my 2021 taxes on TurboTax and had done a substantial Roth conversion in Dec 2021. I made an estimated tax payment by Jan 15th to cover it. When you input your data for your estimated tax payments, the dates that you made the payments are needed, that way the Form 2210 program can account for if you paid on time.
The exception is the safe harbor rule. If you make four equal quarterly tax payments that cover last year's tax liability (110% for high income), then you can pay the additional taxes for your Roth conversion when you file next year.
