I don't think facebook needs some kind of age verification scheme at all. They are already fully aware of how old their users are. The kids post photos and messages every birthday. They use these platforms talk with their school friends. The platforms know who the children are. They already target them with ads and algorithmic manipulations accordingly. They don't need our biometric data to know that we're adults, they just want it anyway and this is their excuse.
WRT to how it was done in Australia.
"Meta, which owns Facebook, Instagram and Threads, began closing teen accounts from 4 December last year. It said anyone mistakenly kicked off could use government ID or provide a video selfie to prove their age."
So the bulk is done as you say but they still need* an age verification system for when they over-stepped.
* need here is because of the way the laws were written AFAIK.
Platforms can't know what the false positive and false negative rates are simply from cases where a user is thought to be a minor and proves otherwise. Even if the law were written better, for example to say that 95% accuracy is acceptable, platforms would still have to verify id from at least a random sampling of thought-to-be-adult users, which doesn't help you if you're one of the ones randomly selected.
We need some kind of verification system that gives no extra information about users to the platforms, but I don't know if there's a true ZK way; it might require government involvement. I think that's fine. Govts could certainly run an age-verification system, give a signed yes or no token back to the user, with some permanently applied jitter per person so that platforms can't use cookies from returning users to figure out their birthday. As long as the government program has strict oversight to ensure it's not saving information about who's visiting what sites, it seems fine, or at least vastly better than entrusting photos of IDs to private 3rd parties.