I got curious about this and checked and insanely there is no easy way to do this. Weird omission for sure.Orrrr, Apple Music could just have a button "Download all Music in Library".
My approach is to take the "Favorite Songs" playlist that Music generates and set that to download. That way any track I favorite is available offline. Works pretty well for me, and doesn't overwhelm my storage the way downloading everything would.
One workaround for keeping ALL tracks downloaded would be to make a Smart Playlist in Music on a Mac that includes all your songs. (Just set some search criteria like "artist is not hhkjdgkjhf" so it catches everything). Then, on your iPhone, set that playlist to download. Irritating, but once you set it up it should just keep itself updated and download tracks. I've set up quite a few smart playlists on my Mac and they all work and update nicely on the phone.
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