"you need to specify for what tax year it is for"
Yes, you have to specify 2021, because you have already exceeded the limit for 2020.
However, time is not linear in the world of HSAs. For example, if you incurred a medical expense in the past that you paid with after-tax dollars, but you incurred this expense AFTER your first HSA was created, then you can reimburse yourself from the HSA now for that expense, even if you did the original payment 5 years ago.
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