The eID of the ePerso supports pseudosignatures, which allows the seller to only get to know “This ePerso belongs to someone of legal age who also knows its PIN” and the state to only know “someone I [the state] authorized to perform age verification did so”. That is privacy-preserving by any reasonable measure.

They’re not. The seller just has to verify customer age, same as when e.g. buying alcohol in the supermarket or entering a gambling hall.

Valve has simply been refusing to do so, even though eID makes privacy-preserving age verification trivial, frankly.