I think this article makes a pretty big leap in the middle. There's really no reason that the operating system needs to be involved in the "Private" solution. It could just as easily be a website or a browser plugin. All you need is your government of choice to have some way to provide a token with whatever important bits necessary in it ("Yes this person is over 18 and a resident of WA"). You could even have third party sites/libraries that could read that token and verify what it contains.
The last third of the article is all based on that giant leap.
I have something that looks like that. Mine is a bone mounted hearing aid. Usually there’s a little device plugged into it.