I wanted to add: I suspect part of the issue is that the new iPhone is causing a lot of people to log into the apple accounts, and there's way more traffic than their infrastructure can support. Obviously, Apple should address this.
I was trying to authorize a new computer. I made it in by rapidly clicking enter, but kept getting the 'you have authorized 5, that's all you can have', even after I'd deauthorized 3 machines no longer in use. BUT there was still a number 5 in parenthesis after my iPad. De- and Re- authorizing it didn't make the number go away, and I think the apple system saw the 5 (that they themselves had put there) and didn't actually look at the number of computers.
I manually renamed the iPad without the number, did another session of clicking enter on the machine I was trying to authorize, and suddenly, everything worked! My playlists and thousands of songs were suddenly available on my Windows machine.
My primary goal was ripping CDs most of which are non-commercial enough not to be available streaming. Apple music no longer supports importing, so I still needed iTunes for that, but once the computer was authorized, almost all of that was automatically available.
Once it worked, it worked seamlessly and was worth all the hassle.