I understand all that and I know how to set the audio quality. But when you have Dolby Atmos enabled it only says “Dolby Atmos” on the song. It doesn’t tell you what quality it is unless Dolby Atmos is off. If Dolby Atmos is off then the song will either say “Lossless” or “Hi-res Lossless”. I guess there isn’t a way to see the audio quality on the song with Dolby Atmos enabled right now. If so there should be two tags per song like “Dolby Atmos + Lossless” or “Dolby Atmos + Hi-res Lossless”
I don't plan to use lossless, so I have not turned it on. Thus, I didn't observe what you described. But yes, it makes sense. Since you're asking specifically about downloaded songs, you can see the file type in the Song view on macOS.
With lossless turned off or turned on but set to High Quality AAC 256 kbps , my downloaded files are identified as "Apple Music AAC Audio File". When I turned on lossless and choose lossless, they identify as "HLS media".
I'm guessing Dolby Atmos is using the same format as on video, namely lossy encoding using 768kbps DD+ as its base transported over MAT 2.0 (I hope they do TrueHD Atmos at some stage...)