Payments to Apple Credit Card

You don't. You set up your backing information in Apple Card and payments are made through Apple Wallet with Apple Card. You'll be notified when a payment is due. For example, anything you charge in the Month of September, is due October 31st. You make the payment through Apple Wallet, then deduct the payment you made through your checkbook.

Otherwise, there is no current way to set this through online bill pay.

Feel free to make a feature request to Apple about this: Feedback - iPhone - Apple

If it's not an option there, then it's not an option.

Not liking the answer does not make it wrong.

You can't do that.

How to make Apple Card payments

This is really how Apple and Goldman Saks set this up.

You're welcome.