I expect a lot of comments on this article to be varieties of "this is terrible"... but it's really not, and I happen to have significant knowledge here. There is a big caveat, though, which I'll explain below.
First, the basic thing that makes strong, reliable age verification possible in the EU is national ID cards. In every EU country, as far as I know, you can get a national ID card basically from birth. A few issue at birth by default, but even those that don't allow parents to apply for cards for their kids at basically any age, and it's not uncommon.
I get the widespread American resistance to a national ID card, but I really think it's misplaced. There are risks, yes, but on balance the benefits are far larger.
Second, when the EU says you can verify your age without revealing your identity, they seriously mean it. I worked on the ISO 18013-5 mobile driving license standard, and its protocol is the basis for the age verification scheme (18013-5 also supports privacy-preserving age verification). The protocol enables cryptographically-secure privacy-preserving age verification, providing, essentially, a single cryptographically-verifiable bit answering the question "Is this person over age X", for specific legally-important ages. A great deal of effort goes into ensuring that the keys used to sign the bit cannot be linked to the identity of the person. One important element of that is the signing keys are single-use, so if your prove your age to two different web sites, they can't compare notes and notice that your proof of age used the same signing key, thereby proving that whoever you are, you visited both.
Note that under the 18013-5 design, if the verifier (e.g. the web site receiving proof of age) could collaborate with the issuer (the government), they could deanonoymize the holder (the person proving their age). Work is ongoing to devise protocols using group signatures or other cryptographic constructs that make verifier/issuer collusion fruitless. It's been a couple of years since I worked in this space, so I don't know if those new approaches have gone into production, but if they haven't, they will.
The big caveat I mentioned at the top is that there is no way for these systems to verify that the person who is providing age verification is the legitimate holder of the national ID upon which it's based. That is, a kid can steal their dad's ID and use it. Because the age verification is truly, strongly anonymous, there is no way for anyone to detect or prevent this... yet.
The "yet" is because people are working on incorporating privacy-preserving biometric authentication into the scheme. This is a little tricky because to provide privacy it's critical that the biometric acquisition and matching happen entirely in the user's device (or in the chip in the national ID card). But it can be done. Making it sufficiently secure, sufficiently reliable and sufficiently cheap is a significant engineering challenge, but it's being worked on. In another decade or so, the caveat may be removed.
If all of this seems silly to you... well, the age verification for porn may be, but the privacy-preserving selective proof technologies are general-purpose, and able to answer any age verification question any many other useful questions in a strongly privacy-preserving way. In any case where you need to prove something about yourself (age, city of residence, driving privileges, etc.) right now you need to provide the complete contents of your ID, which reveals far more about you than is necessary. The combination of cryptography, secure hardware and clever protocols used in this age verification can fix that, generally, enabling us to identify, authenticate or prove things about ourselves with only the minimal information absolutely necessary. It's a good thing.
And, honestly, it's a good idea to keep very young children away from porn.