To access iTunes Home Sharing content, you need to use the Computers app on Apple TV.
The Music app is for iTunes Match subscription, and/or iTunes Store content, but not Home Sharing.
On newer models, the Music app is also used for Apple Music subscriptions.
Use Home Sharing to share iTunes content with other devices - Apple Support
Apple Music subscription tracks can not be shared with Home Sharing.
If you have trouble locating the Computers app, then try looking further down the icon list on the Home Screen, as it may have been moved when the Apple TV app appeared with the latest update. You may relocate it towards the top, if you want.