"For 2022 - I can rollover the HSA contributions and earnings from 2022 into 2023."
To be clear, this is not a rollover. "Rollover" has a different, specific meaning with regard to HSAs. This is a return of your 2022 contribution made no later than October 16, 2023, accompanied by attributable earnings, and that cash is subsequently applied as a 2023 HSA contribution. (The October 16, 2023 deadline only applies if you filed your 2022 tax return or requested a filing extension by April 18, 2023, or you an in a federally-declared disaster area that has had the filing deadline changed to October 16, otherwise the deadline was April 18, 2023.)
"For 2021 - since the 2021 tax deadline filing has passed I can't withdraw my excess contribution for the last 6 months of 2021. In this case, I have to pay income tax and then a 6% penalty for 2021, 2022, and 2023 (since my 2022 rollover will max out my contribution). Then in 2024, only make contributions that add up to the limit from - the $1800 from the last 6 months of 2021, the possible 2022 overage from above, and the rest as regular contributions?"
What you propose makes sense. Your other option is to take a taxable distribution in 2023 of exactly the amount of the 2021 excess, $1,800, but that would be subject to a 20% extra tax if you are under age 65 (which is likely since most people become ineligible for an HSA contribution after age 64 due to signing up for Medicare). That would be more than the 6% you would pay by leaving it in for 2023.
