Your IRA custodian will send you a 1099-R with distribution codes that will identify the distribution as the return of excess IRA contributions - when you enter this into your 2023 return, that is how you will report it. Anything on your 2022 return vis-a-vis the excess was handled automatically by TurboTax when you told TurboTax that you wanted the excess withdrawn.
I see. I don't expect to receive that form anytime soon so does that mean I'll have to file an amended return?
No, no amended return for Tax Year 2022 needed.
TurboTax knows that that you are withdrawing the excess for 2022., so the contribution for 2022 will be automatically limited to the correct amount.
The return of the excess is not a taxable event, and your 2022 return will be correct. There is no penalty on the excess because you withdrew it in time.
The 1099-R will be entered on your 2023 return. That's not a taxable event, either, but you enter it so that the IRS won't wonder why you didn't report a 1099-R on your 2023 return.
If that is the case, do I need to report that I made an excess contribution and then also that I withdrew it before the deadline?
If I do need to report the withdrawal amount-in my case $6000-would that be the amount I enter into TT or do I also need to include the withheld taxes and/or any interest that accrued from that contribution?
TurboTax already knows (and told you) that you made an excess contribution to your IRA. TurboTax automatically took steps to limit your contribution to the correct amount.
Other than telling TurboTax how much you will withdraw, and whether or not the withdrawal will be before the due date, you don't have anything else to do.
Let TurboTax do the work for you.