"my HSA distributions totaled $2537.57 which included the excess distribution of $681," - Are you saying that you actually withdrew the $681 before the due date of the 2022 return (i.e., April 15, 2023)?
When you withdrew that $681, did you tell the HSA custodian that it was for "withdrawal of excess contributions"?
If you withdrew this amount by the due date of April 15, 2023, then, yes, going back and amending 2022 would be a good idea, because that would erase the "long-term excess" (my term) that got taxed at 6% and carried to 2023.
Since the long-term excess is appearing on line 2 on your 2023 8889, erasing it would likely erase any excess for 2023. Then you would be done with it.
So, did you withdraw the $681 before April 15, 2023?
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