Same exact thing. Phone is fine. Computer is far from it. I've tried signing out and in, turning iCloud music on and off, etc. and same thing. I also signed out/icloud off on phone and then signed back in/turned iCloud back on and it had no trouble bringing back my library, but computer just refuses to. i read a forum from a few years ago where someone was getting the same icon and eventually it just started working and seemed to be server side, but its annoying because the apple status website says everything is fine.
David - did you do anything big to your library right before it stopped working? I had just reset the play count on all 20k + songs to 0 (fresh start...) so the only thing i can think of is the servers didn't like how much activity i had going on. And i appear to have lost my connection halfway through that, because on my phone the play count only reset on like half of my songs (i know that from looking at my most played list - about half of them are still on three, and then the other half of that playlist are just the first songs in my library. so maybe i'm just in time out for some indefinite period of time, but if so - that's stupid.