Unfortunately. you were hit by the curse of the dynamic screen sequence in TurboTax. That is, the next screen you see if often determined by the last thing you entered. This sometimes makes it impossible to find the screen that you want.
So no HDHP at all in 2023. If you had not answered YES to the Medicare screen, the next (I think) would have been the "Was [name] covered by a High Deductible Health Plan (HDHP) in 2023?". Oh well, you were able to add the months as Medicare or NONE, so all's well.
Despite all this, I haven't answered one of your initial questions: "As soon as I do this, my estimated Federal and State (MA) returns reduce by several thousand $s."
This is because I don't know the answer - your path is a bit unusual, and I don't know what TurboTax was thinking at the time - and yes, TurboTax often does things in the background that are mysterious (correct but mysterious). I would often suggest that people not watch the Refund Meter too closely, because it would just upset them, and they would confuse a temporary result with the end result. Especially in the HSA interview, there are several place where the refund spikes and the user is puzzled and upset, yet two screens later, that is all undone.
So the important thing for you is to examine the final return and see if it makes sense.
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