The cryptography that Apple uses for _their users_ is something novel and useful. I'm sure there would be completely open solutions that doesn't require Apple servers. At the moment this is Apple specific. I'm guessing most users will user Apple/Google solutions (just like how Passkeys are being used today) but for the security and privacy conscious there is always ways to keep your own private keys. Most people are handing over their private keys to Google and Apple for Passkeys today. That's not necessary a bad thing. Most people reuse passwords so it's an improvement.
If Apples solution only tell the site that the current user has an verified apple account without providing futher info I guess I can be acceptable for most. If the site being visited get info about whom that specific user it is a no-go.
On a more meta level it is tragic that we wont be able to use our computer online without being signed in to an online and be verified.
No thank you. Do not want.
PS: I stopped reading the apple support article after reading that sentence.