"Will these paid out of pocket expenses offset the refund I will receive and I wouldn't have to report the HSA refund as a taxable event?"
Yes, just document what happened - the refunds, and each payment for the out-of-pocket expenses, in case anyone ever asks.
If you would not have had these out-of-pocket expenses, you could have filed a Mistaken Distribution request for the 2023 amount amounts. I don't think an HSA custodian would allow such a process for 2022 and before.
So it looks like it was a good thing that you had these out-of-pocket expenses.
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