No, do not include the federal withholding unless a corrected W-2 is received. You must report the distribution on the 2022 tax return along with the federal withholding assuming you do not receive a corrected W-2 for 2021, which is unlikely. You will receive the Form 1099-R, as you indicated and you will report it in 2022 if no correction is made to reflect the correct amounts on the 2021 W-2.
The codes in Box 7 on the Form 1099-R will determine the taxability of the income for 2022.
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