Shouldn't the federal income tax withheld in a Form 1099-R be included in the amount of Taxes Paid in the breakdown? It's only calculating with taxes withheld from W-2s.

Isn't it a 2022 1099R?  Check your actual 1040 line 25b for the withholding.  

It is on your Form 1040 on Line 25b

It's blank.

It's supposed to be a 2023 1099-R. Line 25b is blank on the 1040.

Then the 1099R goes on your return next year.  @dmertz 

TurboTax says I need to put it in this year's as well. I over-contributed to my 401k in 2022 and received the excess deferral in 2023. TurboTax says I should follow these steps when it noticed I over-contributed:

1. Report the excess deferral on your 2022 return in the Income section for Retirement Plans and Social Security whether or not you received a Form 1099-R before you file your return. Enter as much information as you can. Report the excess deferral amount in boxes 1 and 2a, and use code P in box 7. Indicate that this is a 2023 Form 1099-R.

2. In 2023 (Typo? I assume it meant 2024), you will probably receive two Forms 1099-R. One reports the excess deferral amount. The other reports the earnings on the excess deferral. Enter both of these forms in your 2023 return, and we'll only add the earnings to your 2023 income.

I actually haven't received the 1099-Rs since I'm supposed to get it next year. I filled in the income for retirement plans like it said, but even though the excess income is being calculated in the gross income, the federal tax withheld field isn't calculated in total payments.

I found this post:

https://ttlc.intuit.com/turbotax-support/en-us/help-article/form-1099-r/401-k-excess-deferral/L9XUjVAxP_US_en_US

The withholding will be applied on the 2023 return. I suppose I'll just wait until next year and amend the 2022 return instead.

Right.  It's for this reason that having taxes withheld on a return of contribution reported with code P is generally a bad idea.  The year that the income must be reported does not correspond to the year that the withholding is credited.