After disabling Apple Music again completely, I purchased three songs (with a different AppleID to boot) that I had added to 'My Music' while trying out the service. The first one downloaded fine and showed up in my library, the other two didn't show up in my library. In the iTunes Store they were labelled as purchased (in place of the price tag) but trying to check for available downloads from the store didn't find anything. What had happened is that I had downloaded those two songs to make them available offline during my time using Apple Music. After I had disabled Apple Music, those two songs (maybe others as well) stayed on my Mac for whatever reason; they were right there inside the iTunes library folder visible in the Finder. Trying to import the two files into iTunes, I was greeted with a popup screen saying that I could not play the songs because I wasn't logged into Apple Music. Clearly, some sort of metadata or DRM told iTunes that these were songs from the streaming service and thus couldn't be played without being logged in. Their presence very likely prevented the download of the new files from the store (or they got downloaded but still got tagged with those metadata). Almost accidentally I hit the spacebar with one of the songs selected and it started playing. It also played in third-party apps, suggesting that the files themselves were without DRM and that iTunes was labelling them as unplayable. The solution was to simply re-save the audio files (I tried various options, settling on QuickTime 7 and a passthrough to avoid re-encoding) and import them into iTunes.