You must double click the side button to initiate an Apple Pay transaction and that is followed by verification with FaceID/TouchID or Passcode. That sends the unique code to the merchant that was provided by your bank when you added to card so the merchant does not have your actual account number. The transaction actually flows from the bank of the issuing card to the PNO (VISA, MasterCard, American Express, etc) to the merchant and does not involve Apple at all.
Only you can give that consent unless you have given your Passcode to someone else and that would authorize them to make purchases with your device. If you are receiving recurring charges from a merchant, that is handled like any other credit card transactions where you first contact the merchant and if unresolved dispute the charge with the credit card being billed. No money is transferred to Apple.