During checkout twitch states that it may use a saved payment information for reoccurring bills, but there is consent or even mention that the current one time payment method will be stored long term. (Beside record keeping which is not the full payment information, even the linked privacy notice does not mention, which would also be against GDPR as it forbids bundled consent with general terms)

This is against GDPR Article 6(1)(b) and Article 6(1)(F).
EDPB clearly states that for the optional storage of credit card data to facilitate future purchases, the only valid legal basis is explicit consent under Article 6(1)(a)

A clear consent checkbox need to be there for one time purchase,
and a clear statement for payment method will be stored need to be there when a reoccurring purchase takes place.