Apparently all the songs I have purchased aren't in iTunes. I can see the content that hasn't been downloaded by going to the "iTunes Store" tab, then clicking on the "Purchased" link, then selecting "Not in my library". At that point I can select each album one at a time and add it to the downloads list. It won't let me select more than one album at a time, although if there are multiple albums under a given name, I can switch to song view and download all songs for a particular artist at once.
This isn't acceptable as there are several albums for every letter of the alphabet, and periodically there is some error and I have to manually retry/restart a download. Furthermore, some albums have multiple artists, and I can't even download a single album in one click, I have to click on each artist separately to get their songs from that album.
How can I have it all download in one go?
This question has an answer, but I can't find the "All iCloud Music" graphic it shows.