Please do not remove excess HSA contributions until TurboTax tells you the amount to remove - the reason is that taxpayers frequently miscalculate the amount that is in excess and removing amounts that were not in excess can cause more tax.
Since you referred to a 10% tax, I assume that this came from lines 18 through 21 on your 8889 (not your spouse's). Since I believe you were hit with a 10% tax because of a "failure to maintain HDHP coverage", let me explain how this works so that you can apply it to your situation (I don't have enough information about to know how it fully applies in your case).
When you do not have HDHP coverage for the entire year, but do have HDHP coverage on December 1st, then you are able to use the "last-month rule". This rule allows you to use the full annual HSA contribution limit, no matter how few months you had coverage.
The "catch" is that you must keep HDHP coverage for the next year, or the previous year is recalculated as if you did not have the higher limit, and you pay 10% tax in addition.
So, my assumption is that you started your HDHP coverage in 2021 after January 1st, but was covered on December 1st - this triggered the last-month rule. However, since you did not have HDHP coverage for all of 2022, the additional tax and penalty processing for lines18 through 21 was triggered.
For 2022 to 2023 (your final question), the last-month rule would be triggered again only if you did not have HDHP coverage for all 12 months (as you evidently did not), but also if you did have HDHP coverage on December 1st for 2022 (I can't tell if you did or not).
Let us know which months you had HDHP coverage for 2022.
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