In the system the EU is using you are the broker in the middle.

Briefly, your government issues you a digital copy of your identity documents cryptographically bound to a hardware security module that you provide. For the first iteration this will be the security module in your smartphone. Later iterations will support standalone smart cards and plug in security modules like YubiKeys.

If you wish to prove your age to a site a cryptographic protocol takes place between you and the site which demonstrates to the site that you have a government issued identity document that is bound to a hardware security module, and that you have that module, and that the module is unlocked, and that the identity document says that your age is above the site's minimum age requirement.

No information is transmitted to the site from the identity document other than the age is above the threshold. There is also nothing transmitted that identities the particular hardware security module.