Ok, so I had the same problem.
A few days later I tried again - and it worked.
(???)
Two factor auth has been on for years, by now...
However, I can't turn on "Advanced Data Protection" as it's not available in my region (Switzerland).
My guess:
a) Apple's servers are overloaded? unlikely though
b) bug. Would definitely not be the only one, the public release of the latest iOS feels like an early developer beta to me - plenty of bugs.
c) not actually available in all countries yet, and all the help & documentation is outdated or wrong
Very strange that the *verification* fails - and that it doesn't just tell the user in the first place why it's not possible to activate the key