Taxes withheld from the withdrawal from the 401(k) are tax payments reported on your tax return along with the gross amount of the withdrawal. Your tax liability is based on your total income from all sources when completing the return.
You will receive a Form 1099-R from the plan in January of 2024. You report the Form 1099-R received on the federal tax return with the taxes withheld reported as a tax payment on the Form 1040. No different then reporting a W-2 on your tax return.
