Using the All Speakers and TVs selector, Apple Music running on iOS/iPadOS/macOS functions as a remote for Apple Music running on the ATV, functioning more or less (more less than more, but hey) like Spotify Connect.
I use an HDMI splitter after the ATV, shifting all audio via eARC to my KEF LS60 and all video to my TV. Something similar can be achieved with a splitter separating the audio signal to optical or coaxial. Finally a well working (and inexpensive) way for playing the Apple Music signal on the stereo unmutilated.
Note: this functionality is new for tvOS 27 expected in September (first developer beta released yesterday, public beta expected next month). Yay for progress, I guess.