1. Were you capable of being claimed as a dependent for all year (you don't do dependent month by month)? If so, you are not eligible to make any contributions to your HSA at any point during the year.
2. When you are not under HDHP coverage with no conflicting elements, like Medicare, or other employer insurance, or being a dependent, then you enter Self or Family (depending on what HDHP you have), and NONE in every other case (except when you have Medicare).
3. Since you can be claimed as a dependent for the year (whether or not you actually are), when you see the question, "Was [name] covered by a High Deductible Health Plan (HDHP) in 2023?", answer "No, I did not have coverage." The fact that you had an HSA is irrelevant, as well as the fact that you had HDHP coverage.
4. If you say "No, I did not have coverage", you won't be asked for month by month coverage.
5. The only catch will be that during the Federal Review, TurboTax will get confused on why you are in the form 8889 when you don't have any HDHP coverage. The Review then asks you what entry do you want to put on line 1: Self or Family?
6. Since you have already said that you had no coverage, entering Self won't hurt anything, but it will get you past this Review question.
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