How do I request a refund for a online purchase and used Apple Pay to buy

You'll need to contact the store you made the purchase on and request a refund through their own refund mechanism. Apple Pay is a payment conduit only and has no way of refunding you anything directly.

Link-> Get a refund for purchases made with credit or debit cards using Apple Pay - Apple Support

Again, you need to go to the online source you got it from and request a refund through them.

If it was a person or eBay, then you need to process through the person directly or Ebay.