The UK age verification seems to be "Upload your ID to a porn site", but that's not the EU solution from what I can tell. What the EU is building is an Identity Wallet, where your national online ID verifies your age with your wallet. The wallet can then tell the sites that yes, this person is in fact 16+ or whatever the age restriction is. How they plan to avoid having kids just borrow their parents phones I don't know, frequent reconfirmation maybe?

The mistake that UK, and probably others, have made is that the government isn't actually able to provide the required infrastructure.

If the solution is anonymous in the sense that the government doesn't see that I visit some site, and the site doesn't see who I am, then I struggle to see problem. This assumes that it's only applied to services and products that are already age restricted in the physical world already.