I too, am having this same issue.
Just got an external DAC and headphones today, and was excited to try out Hi-Res Lossless on Apple Music. My setup is done, and I noticed that Apple Music does not always play Hi-Res Lossless, even if the album is supported.
For example, let's take Journey's Greatest Hits album, which supports Hi-Res Lossless. I'll search for "Journey" in Apple Music, click on the Greatest Hits album and play a track. When playing a track, I noticed that the "Lossless logo" is not present in the track bar. See below.
However, if I click on the three dots of the song that is currently playing and go to "Show Album in Library"
And then I play any track after selecting "Show Album in Library", that track will play in Hi-Res Lossless.
I've read another post where Re-authorizing (Go to Account>Authorizations>Authorize this computer) your computer might help. For me, it did not work though.
What I noticed helps sometimes is deleting an album from my library and the re-adding it and try playing it again, and then it will sometimes automatically play Hi-Res Lossless. Most of the time I still have to go to “Show Album in Library” for it to play Hi-Res Lossless.
I was testing out different Hi-Res Lossless songs and I played Yellow by Coldplay. It wasn’t playing in Hi-Res (although it should have been) and I was curious to see the info on it. I went to “Get Info” and then I noticed It was linking me to the Yellow in their Live 2012 album rather than the Yellow in their Parachutes album (which is where I was playing it from). I even went to “Show Album in Library” and it brought me to the Live 2012 album rather than Parachutes. I fixed it by deleting both albums from my Library and then adding them back. But they still don’t play Hi-Res automatically 🤦🏻♂️
Seems like a number of issues on the Music app on macOS...