The credit card details are not stored on my side.
The easiest way to change your credit card details, is to just renew one or more of your subscriptions manually. That will add a year to the subscription.
All renewals will use the credit card details (mandate) of your last payment.
I see no way to change credit card info whether I do an automatic renewal or a manual renewal. The credit card account I used when renewing last time will fail if charged.