"Currently in Initial Enrollment Period for Medicare, I will not start Medicare till 2023 or 2024." - What does this mean? Are you enrolling in Medicare now or not?
Note that if you enroll in Medicare more than 6 months after your 65th birthday, then the Social Security Administration back dates your coverage by 6 months. In such as situation, your Medicare coverage begins at the backdated date. Thus if you apply for Medicare in January 2023, and you are more than 65 1/2 years old, then the SSA will backdate your coverage to July 2022, which means you have to account for this in determining your 2020 HSA contribution limit.
I don't understand your exact dates so see if you can apply what U just said to your situation.
NOTE: don't worry about which months the actual contributions are in; instead worry about how you calculate the annual HSA contribution limit. TurboTax, of course, will do this for you when you enter the data on the return, but you, of course, want to know what the limit is before the year begins (which is why you are asking)..So, pick a date in which you will enroll in Medicare (on the first of a month), then backdate it 6 months (if you are beyond 65 1/2) to determine which months that you have only your spouse's HDHP coverage and no conflicting Medicare coverage.
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