The date is to determine if you are paying on time by April 15 or late. You can enter 4/15/2025 if you plan to pay by then. You can file an extension for your paperwork, but not the payment.
I agree with fanfare that you should make your IRS Payments online and then select that you will mail the amount when finishing the return. Obviously, you would not mail anything since you paid online.
You can submit a bank draft or you can mail a payment. I strongly advise against putting a check in the mail.