Your W-2 and 5498 won't change, because they report what actually happened in 2020.
After Turbotax tells you that you contributed an excess amount, it should ask if you will remove it before the tax filing deadline, or choose to leave it in the account and pay the penalty. When you indicate that you removed the excess, Turbotax will make the correct changes to your tax form. The withdrawal of excess will be reported to the IRS, so everything will match up in the end and you shouldn't get any nasty letters from them. If your account earns interest, the interest on the excess also needs to be withdrawn, and that will be reported as taxable interest income on your 2021 return, since it was actually paid to you in 2021.
By the way, a withdrawal of excess contribution is not a normal withdrawal and probably requires extra paperwork at the HSA bank. If you just did a regular withdrawal, you messed it up. You will need to put that money back (a "return of mistaken distribution" which is also a special procedure) and then make a correct "withdrawal of excess contribution."
