cancellation of a payment method for a subscription that I no longer want to have

You need to add a new payment method so the charge that you previously authorized can proceed, then you can remove the old payment method. It is not possible to cancel a previously authorized charge and you also cannot request a refund on a pending charge.

Charges are authorized when you double click the side button with the amount showing on the screen followed by verification with Face ID or Passcode. That is your agreement to pay for that service. Cancelling the subscription will then prevent the subscription from renewing again the next time.