@mhoye I'm no fan of pointless age discrimination nor locking down all the fun stuff on the internet, but what you're saying here is .. hyperbole. And is actively muddying the subject by mixing a good-and-minimal solution with a worse-and-invasive fallback.
Websites already decide when to gate access. Usually they only do when there's a subscription relationship. Sometimes they do for other reasons like geoblocking, or traffic throttling, or having a national ID card or tax ID number or health card or whatever, or simply private member sites without public access. All totally normal and neither a threat to democracy nor anything likely to change. Every site decides who and when to serve or deny.
Some sites have content harmful to minors. We can debate this but most parents feel pretty strongly about this and at the moment we live in a world where parents both have a legal duty of care for minors, and vote. So they want to express their duty of care through legislation about this.
The sites with harmful stuff being forced to block minors could use the age they already estimate for their users. Those estimates are not bad. But they're noisy -- 13-vs-18 is probably within the noise -- and more importantly users are incentivized to lie and inject noise and generally make that signal bad. So the sites being forced to do this type gating are in a bind.
Conveniently though, the parents who have a duty of care for minors _also_ happen to usually own and administer the phones (it's always phones, linux is completely beside the point) that minors use, so they can set a bit of out-of-band admin-only metadata on the account of the device that says "minor". The device can attest that in ways 99% of minors won't be able to circumvent, and it sharpens the signal and the block works better.
This is much, much better than the alternative of "demanding everyone use a 3rd party identity verification service that winds up with a mass of everyone's passport photos and also a list of all the websites they visit".
It also doesn't relate to any of the other axes of identity-gating you're discussing. No duty-of-care relationships, no noisy signal with an important law mandating a sharp answer, no other-person-owns-your-machine. It's a special case that there's little reason to believe will generalize much.
IOW there very much _is_ "something special about age as a differentiator": in the legal rights and responsibilities around parenting _and_ in the parental device-control that lets the problem get solved relatively non-invasively.