Retirement tax questions

From what you state, you appear to be eligible to claim the credit. 

The CP notice probably stems from two things:

• The IRS is most likely looking for the credit on Schedule 3, line 13d.  (Note that, under Repayment over $3,000 in Publication 525, the IRS advises claiming the credit on this line for 2021 repayment.  I'm not sure why the text specifically limits it to this year, since the line is available in tax year 2022.)
• You identified the type of credit simply as "tax", and the IRS needed more to go on.  It's looking for fraudulent-type claims on this line.      See Internal Revenue Manual 3.12.3.30.10.8, Schedule 3, Line 13z, Write-in Credit (EC 358). 

It wouldn't be a bad idea to contact the IRS by phone before sending in information, using the contact information in the TurboTax Help article I got a CP12 notice from the IRS.  The IRS probably won't be able to solve the issue over the phone -- as you've noted, there's a somewhat complicated calculation involved -- but they'll be able to advise you on what you need to do to resolve your credit issue. 

You can also just go ahead and send in your information to the address reflected in your CP12 letter, stating all that you've stated here, and including the calculation page that you've prepared. Provide as much information as you can, so they won't need to contact you for additional data. 

Also see the IRS' Understanding Your CP12 Notice for more information.