Clarification: "but TurboTax automatically added the amount of 2022 excess to your Other Income." - This is true only if the excess contributions came through your employer (code W in box 12 on your W-2).
If the excess contributions were your "personal" (direct) contributions, then the excess are NOT added back to income; instead, the deduction on line 13 on Schedule 1 (1040) is reduced by the excess amount.
My bad, since so many people do contributions through the employer, we tend to forget to list all the possibilities.
"I had made through my employer from March 2022 through Sept 2022. " - OK, did you employer give you a corrected W-2, so that the code W amount was reduced to be less than the annual HSA contribution limit? That would be OK.
"So I had HDHP coverage all of 2022 (and 2023). " - Sadly, in the eyes of the IRS, you did not have HDHP coverage. To have HDHP coverage, you not only need the HDHP coverage, but you can't have any confliction coverage, like Medicare, or normal employee insurance or an FSA or a variety of things.
So the month that you started on Medicare, it was as if your HDHP coverage ceased.
So, did your employer "correct" your W-2 for 2023? Is the code W amount in box 12 adjusted down to account for the time you were under Medicare?
It's possible that depending on what your employer did that there would not appear to be an excess in 2023. Please let me know what your code W amount was for 2023 (if zero, OK).
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