I paid my 2024 balance due with IRS Direct Pay and plan to mail in my return. Is there a way to designate that form of payment on form 1040, or should I simply include the Direct Pay Confirmation page

Tax returns and payments are processed completely separately. There is no need to designate on your Form 1040 how you are paying and you do not need to include your Direct Pay Confirmation page.

You can just tell the software that you will mail a check to pay your tax due so that you can get past that screen.   TurboTax never knows when, how or even if you paid your tax due and does not need to know.   Your online account will always show that you had federal tax due---because that was the result of the return you prepared using the software.