No, you enter the 2022 Form W-2 exactly as received. However, in the HSA section you must answer Yes to the question that asks if your employer told you about any other HSA contributions and enter the portion of the box-12 code-W amount that represents contributions made for 2021 in the corresponding box (the first box). TurboTax will then exclude this portion from line 9 of your 2022 Form 8889.
(In 2021 TurboTax you should have also answered Yes to the question and should have entered this portion in the box indicating the amount of HSA contributions not reported on your 2021 W-2 (the third box). TurboTax would then have included this amount on line 9 of your 2021 Form 8889.)
