" I moved the excess contributions to 2023 using my.healthequity.com."
It's not clear what you mean by this. However, I think you mean that in 2023 by the due date of your tax return, including extensions, you requested that the excess contribution be returned and that the cash you received from doing so (an amount adjusted for investment gain or loss attributable to the excess) be applied as a contribution for 2023. In that case you should be telling 2022 TurboTax that you had the excess returned and you should be telling 2023 TurboTax that the cash you applied for 2023 is part of your personal HSA contribution for 2023. Nothing about a contribution for 2023 is reportable on a 2022 tax return.
If this is what you did, near the end of January 2024 you should be receiving a 2023 Form 1099-SA with code 2 in box 3.
