TT shows "accepted" state taxes filed 4/12/24. As of 4/22/24 State shows no taxes have been filed. Was I suppose to print and mail the pmnt coupon even though return shows I'm paying w/checking acct draft? Federal owed drafted fine.

You can check that your return was received by the taxing authority  using these instructions: Check the Electronic Postmark of your Return. Pay close attention to the separate lines for Federal and State. They are separate statuses.

If your state was not filed, there is no way the draft payment would have happened.