I agree that for the system to be anonymous the state has to live up to its commitment to anonymity. Have you read the EU’s regulation about this? In there is exactly a commitment that age verification has to be anonymous.

But, let’s take a reality check here:

• For the vast majority of the population, their ISP already collects every single website they visit.
• if the state wants to know what you’ve searched for and where you’ve been online, they already have that data stored. They can only access it legally with a court order.

Yes you can circumvent this logging (to some extent) through VPN - just like you can circumvent the requirement to verify your age with a VPN. But the vast majority don’t.

the only way to have privacy-preserving age checks is when there's a variable on the phone that stores whether the user is old enough. and gives that data forward to apps/websites trying to do age checks.

that variable can only be changed if you're the rightful owner of the device, i.e. if you paid for it and have a code that's on the purchase bill or sth. and children wouldn't have access to that.