my iPhone won't let me update my payment methods

you can try doing it from other means than your phone to verify if the phone and not the method of payment is the culprit

Change, add, or remove Apple ID payment methods - Apple Support

Rickigirl wrote:

but when I go to edit it

I don’t know where you see “Edit.”

I go to Settings > Wallet & Apple Pay > [a card] ... and there when I scroll down, I see “Remove this card”.