How do I fix Apple Music "Cloud Music Library is not responding"?
After wrestling with this all day, even after iTunes status showed normal, I found this solution:


Open iTunes.
Press ⌘-, to open the Preferences dialog.
Uncheck Show Apple Music, acknowledge the dialog advising you you will stop using iCloud Music Library, then select OK.
Reopen the Preferences dialog.
Check Show Apple Music again as well as iCloud Music Library, then select OK.


This will restore iCloud Music Library.  Note: I could not immediately add music to my library after this without seeing more errors, but the next morning I found my add attempt had succeeded and everything seems to be in good shape.