"The year 2023 1099R (from the 401K administrator) for the 401K distribution to the traditional IRA with the employee contribution after-tax amount of $400 in Box 5 (or the data on the 1099R?) was supposed to be sent to the IRA administrator (the recipient of the 401K distribution), and the IRA administrator would put into their records to show $400 of the $200,000 transfer is after-tax?"
No, it's your responsibility to track your basis in nondeductible traditional IRA contributions. When you are next required to file Form 8606, you'll add the $400 on line 2 an provide an explanation for this adjustment to your basis as after-tax basis rolled over from an employer plan. Because this rollover of basis is not to be reported on Form 8606 until you are next required to file Form 8606, TurboTax does not automatically make this adjustment. When you do need to file Form 8606 for some other reason, you'll indicate to TurboTax that you made nondeductible contributions to your traditional IRAs, click the EasyGuide button, mark a box to indicate that you moved after-tax basis for an employer plan to your traditional IRAs, then enter the $400 adjustment. TurboTax will then prompt you to enter an explanation of the adjustment.
The investment gains and company match in the traditional 401(k) are pre-tax.
