How do I change my iCloud subscription's payment method with an active subscription?

my iCloud subscription is under a card I no longer have. I want to change it to another card on apple pay, but I can't remove the previous card given how it says there is a "current active subscription" under it. I tried cancelling icloud to then repurchase the subscription, but whenever I switch to the 5g free plan in the downgrade options, after I press "done" nothing happens. Should I wait until the subscription expires to sign again or am I doing something wrong?

[Re-Titled by Moderator]