There’s nothing in the EU age verification structure that requires you to hand more information to the places where you need to verify your age. In fact the system expressly prevents it. Similarly in the ZKP architecture, it it not legal, nor possible, for the age verification service to know where you log in.
Maybe I’ve misunderstood your comment and so I say this in great respect; but if you don’t understand the technical details about the system the EU has defined, you may be basing your resistance on wrong assumptions.