I'm having the same issue. Support documents say "account settings > payment method" should list payment method options, but that does nothing but display a message that "you can change payment method any time" but no way to do that. Thinking it might be a browser issue, I tried on multiple browsers, Mac, Windows, phone...still does not work.
I agree with @Chonk, we should not have to contact technical support for something so basic.
And this is not for a new purchase, it's me renewing my subscription but needing to update my payment info.