I updated to macOS 11.4 Big Sur today and started a free 3-month trial of Apple Music.
After getting the settings in place to play lossless, I am up and running and I see a little icon in the "now playing" pane at the top center that reveals the bit depth and sample rate of the album chosen when clicked. No where ahead of time are you able to see that information, it's just pot luck, pick an album and play it to find out.
In playing several different albums that turned out to be different source sample rates, I see exactly what you were describing the other night, that being the only way to get the sample rate to change is by physically altering it manually in Utilities ➞ Audio MIDI Setup for each album, there is no automatic change of sample rate happening in Apple Music, my external DAC's sample rate indicator confirms it.
Worse yet, even though my BitPerfect plugin seems to be functioning, it too is unable to control the sample rate, arguably the whole reason anyone would have ever used it in the past with iTunes. When BitPerfect is enabled, you do have to select the correct output device (external DAC), so for example after enabling BitPerfect the sound would still come out of the MacBook's own onboard speakers unless I select the external DAC in BitPerfect's settings, however in choosing a 24/96 album, the sample rate is still pinned to what the Audio MIDI Setting is, BitPerfect is unable to override that as it does with iTunes.
So I guess I'll send the BitPerfect developer a note and hope he responds, as I doubt anyone will ever get an answer out of Apple about this, though you'd think they know damn well it is ridiculous for them to expect customers to manually adjust for and select the correct Audio MIDI setting sample rate for each and every album (or track in a playlist). Surely they must have a plan for either Apple Music itself, or the Audio MIDI Setting of sample rate to become automatic with source file played?
Not only would an audio enthusiast not be bothered to make this manual adjustment for each and every album or track in a playlist, but you'd be speaking Martian to anyone in plain clothes if suggesting that's what is required to hear "hi-res" with Apple Music.