I figured out that two options needed to be turned on to get MM to work on my iPad 3 - the more-obvious Music>iCloud Music Library option, and the less-obvious iTunes & App Store>Automatic Downloads>Music option.
After the install of OS9 on the iPad, I activated the first option and signed in, and some of my library started loading. I then switched to the second option and turned it off (it was on by default); one of the artists I own records of had 6 of the 20-odd albums load, and that was it - many of the other artists I have multiple recordings of also didn't fully load, but I didn't worry about it. I read your post, toggled on the second option, and my library fully loaded in short order.
I also recommend toggling one or both options; I toggled off the first option, then toggled it on after a couple of minutes - when I toggled it on, the "Genius" option appeared above it, whereas it had not shown up previously.