"I am told that I can request to withdraw $X for 2019, even though the 2019 tax year has passed. If I go this route, then how do I report this in turbotax?"
Be careful of your terminology. As you and Opus note above, you can no longer "withdraw the excess" for tax year 2019, so don't even use the phrase in conjunction with the tax year 2019 amount.
Instead, now you have two ways to fix the excess for 2019:
1. As Opus noted, your excess from 2019 rolls over (if you didn't withdraw it in time) to tax year 2020. If you do not reduce your regular 2020 HSA contributions, then this will cause an excess for tax year 2020. HOWEVER, this is not an excess that you can withdraw for 2020 - it is still the 2019 excess.
2. You request a distribution from your HSA for the amount of the excess in 2019. This will be sent to you on a 1099-SA (possibly on the same 1099-SA as your distributions for qualified medical expenses). When you enter it though, you indicate that some or all of it was not for qualified medical expenses.
For #1, you can try to wipe out the 2019 excess in 2021 by sharply reducing your HSA contributions. If you can't apply it all to 2021 (because you have already made too much in contributions), then roll over the remaining part to 2022, and be disciplined in your regular HSA contributions to use it up in 2022.
Note that if you try to withdraw what you think is the 2020 excess, TurboTax will catch you and tell you that while you have $X excess for 2020, $Y is from 2019 and cannot be withdrawn.
For #2, when you enter the 1099-SA and indicate some (or all) are not for qualified medical expenses, then the amount that was not for qualified medical expenses (presumably the original 2019 excess) will be added to Other Income by TurboTax, and TurboTax will add a 20% penalty. At this point, the 2019 excess will be finished.
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