My apologies for giving some information in error. Things are a bit more complex and confusing concerning Airplay and how it works with Apple apps vs third party apps.
If streaming music from an iOS Apple Music app and wanting to transfer that music to an Apple TV 4K on the same network, press the Airplay icon at the bottom of the app screen. Airplay compatible devices will appear and the Apple TV 4K should be at the top of the list.
Streaming to a receiver or speakers that support Airplay will mean music is streamed from the device to the receivers and speakers and audio signals capped at the limits of the Airplay spec. But, Airplay also includes control of devices such as the Apple TV 4K.
If you start playing a music selection on your iOS device and want to play that same selection on the Apple TV 4K, select the Apple TV 4K from the list of Airplay Speakers & TVs
.
Now, you can control playback of the music on the Apple TV 4K by going to the bottom of the Airplay screen and clicking on ‘Control Other Speakers & TVs.”
Now, you can switch between controlling music playback of music in the iOS device and the Apple TV 4K using the iOS Apple Music app.
Select the Apple TV 4K and the audio signal will actually come from the Apple TV 4K’s Apple Music app while being controlled by the iOS Apple Music app if set correctly. So Dolby Atmos tracks will be labeled and played as such with just the Apple TV 4K shown at the bottom of the screen as the source device.
If the audio stream is sent from the iOS device to the Apple TV 4K via Airplay, Dolby Atmos is lost as it is not supported over Airplay and the audio stream originating from the iOS device is indicated at the bottom of the screen. Notice that Lossless is indicated and is supported over Airplay.
I am always in front of the system when using the Apple TV 4K and never really use the iOS Apple Music app to control it but find it convenient now to browse Apple Music in iOS for Dolby Atmos albums of interest to me and then have the Apple TV 4K play them without leaving the iOS Apple Music app. Still learnin’. I’m now tinkering with the Apple TV iOS app and other apps using Airplay/Control.