Not necessarily. If age verification could be done by some trusted authority, like a bank perhaps, which simply generated some 'token' (like a large random number) and associated with your real name or a pseudonym (or both), and where this is then sent to some central checking authority for websites, then the porn website would not know as to who you were, and there might hence be no tracking. Just one idea. And the age verification wouldn't just apply to porn but various other things too.
There would still be a trace. A service would send in a request for identity checking. Another service would then do the checking and respond.
That latter service would always know which service did the request and which identity was provided in response.
Neither party could be anonymous because you would need scam detection / prevention.
And off course, all of that would require funds. Somebody is going to have to pay for it.
Almost impossible probably - given that once paid-for material is in the hands of any individual, they can do what they like with it.
Have you ever used netflix? It's a streaming service. There is no "material in the hands of..."
You can't access the media without logging in. And to obtain an account, you need to pay first.
As it stands now, all you need to do is google some sexual term and you'll get page after page after page of porn links.
If porn sites would be streaming services a la netflix, this would not happen.
Given the ability to stay anonymous for those who choose to do so.
You can't have it both ways. There is no "anonymous" in a world with any kind of proper age verification.
And if you wish to go technical.... there actually is no "anonymous" on the internet, full stop.
Given the proper motivation and resources, ultimately you can trace all traffic to any website from any device to an IP. And that IP is going to be linked to an ISP. And that ISP is going to know which client / user of theirs is using that IP. You, as an internet user, can make it exceptionally hard to find out off course... for example by using VPN's etc into other countries so that authorities run into jurisdiction issue etc...
But if we ignore that for a moment and assume access to all systems, then every device, every user is technically completely traceable on the interwebs.