I'm looking for a music player that has a shuffle mode, but instead of playing random tracks, it plays random albums in their entirety before playing another random album. Is there one with such a feature in Solus? I only tried the default Budgie one, Rhythmbox, and it can't do this as far as I can tell. I'll gladly try your recommendations!
Music player recommendation that can play a random album
Audacious does shuffling by album. I don't use that feature, so can't say how well it works, but it's there.
DeaDBeef could be one of the most feature rich music players for Linux and it is in the repository. Not sure if it has exactly what you want. https://deadbeef.sourceforge.io/
lollypop has a random album feature.
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Thanks! Out of these, I think I'll stick with Audacious, I like it best. It seems like a good balance of being lightweight and still having the features I want.
@paracetamol I just tried the feature and it works as expected. 
EDIT: I'm actually on the fence with Lollypop. Well, better to have more choice than not enough!
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Tauon Music Box https://github.com/Taiko2k/TauonMusicBox
Available as a Flatpak
(I have never tried this feature)