Do all EU countries have that? I know our (German) ID works that way, using the FOSS AusweisApp, but I hadn’t heard of it being EU-wide (it should be, though).

Spanish ID cards have had an X. 509 cert inside them for more than 10 years, I use it all the time to sign documents and access government sites. There is already legislation and a push for an EU-wide digital identity wallet that should be up and running this year, look up eidas 2.0 and the EUDI wallet.

That looks like it should make things like privacy compatible age verification "trivial".