Apple TV (third gen) not showing in itunes airplay device list. I restored and reset the ATV, made sure it is on same network, restarted router and computer. Home sharing is on. I can access and play music from my library from the ATV but I can't send music from my macbook to the ATV.
Home Sharing and AirPlay are independent services. But both use the same networking, so it is a good test to see if network settings matter for this.
AirPlay is dependent on having an “Activated” Apple TV box. See Settings﹥General﹥About﹥ to see if it lists “Activation: Failed”. If not, then you should be fine for this. If it does list “Activation: Failed”, then please try signing out for iTunes Store, then immediately sign in again. If “Activation: Failed” persists, then try what user RKG61 posted in discussions.apple.com/thread/253315520.
Also please note that not all streaming services support AirPlay to Apple TV (3rd generation or earlier). Some services block AirPlay to any device. Some services make no effort to support AirPlay specifically. Some services will only AirPlay to newer AirPlay 2-enabled devices. Some services support AirPlay from mobile apps, but not from web browsers on Mac. See the content provider’s website for AirPlay support details.
Please disclose what you were trying to stream.