This is also happening to me; I got my Apple Card account, and switched payment over to that as the Family Organizer. However, I still have the Update Payment Information notification in Settings. When I click the item in settings, I'm taken to anotehr page that says "Update Payment Information - To avoid any interruption to your active subscriptions, update the payment information for your Apple ID." There is a "Continue" button. Clicking the Continue button, I am taken to a dialogue to sign in with my Apple ID. Signing in, I am greeted with the "Manage Payments" screen, and under "Payment Methods", it displays my Apple Card.
There is an Edit button, but it is grayed out. Clicking on the Apple Card does nothing; the only active option from this page is the Back button, which returns me to Account Settings.