If you have an Apple Music subscription, then Screen Mirror App will display music available from this service, as it is accessible through the Music app and is shown in the Music library on your iPhone. However, due to DRM restrictions on music from Apple Music, Screen Mirror App won’t be able to stream it to your Chromecast device.
When attempting to play such a track, you will receive the message: “This song is DRM-protected. Screen Mirror App doesn’t support streaming of DRM-protected files”.