Get your taxes done using TurboTax

"Yes, my W2 box 12 shows W code with $2,000 contribution."

If your employer completed your W-2 correctly, then this $2,000 was removed from Wages in boxes 1, 3, and 5 before your W-2 was printed. You keep repeating, "It's not deducted from my salary...", but it's either included in Wages or it's not. If your employer removed it from Wages when they put the code W amount on there, then it IS "deducted" from your salary. If your employer did not remove the $2,000 from Wages, then they should not have entered the code W amount.

I don't mean to be picky in terminology, but it's important so that we understand each other. 

"because it should be taxed at my marginal rate when I withdraw the cash from HSA."

I have no idea what you are trying to say here. There are two options (leaving aside withdrawal of excess contributions and other specialized cases): (1) spending money from the HSA on qualified medical expenses, in which case you pay no tax on the "cash withdrawn" at all, or (2) taking money out for reasons other than qualified medical expenses, in which case you not only add this distribution to your income but you also pay a 20% penalty (unless you are 65 or older).

"I am actually covered for HDHP plan in November and December. But looks like TurboTax now automatically applies the last-month rule,"

Yes, TurboTax automatically applies the last-month rule. I don't understand your concern here. Are you already not under HDHP coverage? Were you really under HDHP coverage in November and December 2021? If so, why would it be unreasonable to assume that you would not stay under HDHP coverage for 2022?

Besides, let's say that you know that you will not stay under HDHP coverage for all of 2022. Yes, applying the last-month rule to 2021 means that you don't have an excess HSA contribution for 2021 (I'll get to your withdrawal in December 2021 later). In early 2023 when you are doing your 2022 return, only if you did not stay under HDHP coverage (are you sure you won't?) would you add the excess back to income and pay a 10% penalty besides - a year later.

Now for your December 2021 withdrawal of $800, you did not have an "excess HSA contribution" at that point. An HSA is not a regular savings account that you can put money into and take money out of willy-nilly. There are definite rules, which, unfortunately, are not well presented in the IRS Pub 969. You really should not take money out as an excess contribution unless, at tax time, TurboTax or another tax software product tells you that you have an excess. In this case when you withdraw the money, your records and the HSA custodian's will match during an IRS audit - otherwise, they won't.

To the IRS, that $800 withdrawal looks like a withdrawal for purposes other than paying for qualified medical expenses, so not only should the $800 be added to Other Income but you should be penalized 20% on that $800. The only reason that TurboTax did not do this on your 1099-SA is because the HSA custodian took your word that it was an excess contribution, but it wasn't.

You may think I am being a pain, but the truth is - and I have seen it many times here in the Community - that taxpayers don't calculate their annual HSA contribution limit correctly, so they make mistakes when they take it upon themselves to take a withdrawal for the wrong amount.

"This is where I need some suggestions on how to do it properly."

To do it "properly", you will go back and mark HDHP coverage for November and December - if I understand you aright - and contact your HSA custodian and ask them to accept that the $800 was a "mistaken distribution". If they accept this (they don't have to, so be nice), you will send them the $800 and they will issue a corrected 1099-SA.

This is noted in the Instructions for the 1099-SA and 5498-SA on page 1:

"As the trustee or custodian, you do not have to allow beneficiaries to return a mistaken distribution to the HSA. However, if you do allow the return of the mistaken distribution, you may rely on the account beneficiary's statement that the distribution was in fact a mistake. See Notice 2004-50, 2004-33 I.R.B. 196, Q/A-76, available at IRS.gov/irb/ 2004-33_IRB#NOT-2004-50. Do not report the mistaken distribution on Form 1099-SA. Correct any filed Form 1099-SA with the IRS and the account beneficiary as soon as you become aware of the error." (NOTE: these are instructions to your HSA custodian in completing the 1099-SA, not you)