Don't let the pension vs annuity confuse you - they are fundamentally taxed the same way.
"Should I just go ahead and put in the taxable retirement amount for 2021" - Probably not. It sounds like you must have said that you have a qualified plan (like most pensions), so TurboTax is going through the exercise of determining what the taxable amount of your distribution is for 2022.
If you are on the screen that asks "For the years [name] received these distributions, was the amount shown in box 2a of the Form 1099-R used as the taxable amount?", then answer "No, a different amount was taxable."
Then TurboTax will (probably) go through a number of questions to see if the Simplified Method can be used to determine the taxable amount.
NOTE: the purpose of this is in case you made after-tax contributions to your pension while working. If so, when the distribution is returned to you, then any after-tax amounts are not taxed again. But these after-tax amounts are not up front, instead, they are spread over many years - this is what the Simplified Method is doing.
Then, starting next year, you can point back to the 2a amounts for 2022, because it should be the same for many years.
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