I don't know what you're describing here, sounds like some variation of contactless payment card standard EMV which, as it's name suggests, is managed by three private payment processors, and it indeed does stores your last transactions.

EU digital id is a smartcard that signs things using its internal processor and it doesn't store any transactions. Even read-only access, e.g. to retrieve biometrics, is protected by a code printed on the physical card, so there's a kind of two factor to access it. It has all the crypto nerd's imagination out there, in an easy to use form factor.