Airplay

How to AirPlay video and mirror your device's screen - Apple Support

If AirPlay or screen mirroring isn’t working on your device - Apple Support

Additionally, verify that both are on the same home network. For Wi-Fi, that should use the same SSID network name. It will not work if your Wi-Fi is split into two by using separate SSID names for the 2.4 GHz and 5 GHz band, and the devices each use a different SSID. Let your router bridge these bands into one logical network.

Are you sure the Channels app on iPhone supports AirPlay to Apple TV? This suggests it does not:

Note: Channels does not support Picture in Picture mode on the iPad or AirPlay on any device due to the video format provided by the HDHomeRun tuners. This is an iOS limitation. [1]

What are you trying to AirPlay? As some content and apps are blocked for AirPlay.

My mobile plan isn’t suitable for hotspot and TV use, mostly because of a monthly cap, so I have not tested such use extensively. I think it should still allow AirPlay for content that is supported for AirPlay.

You may want to contact the app developer for further details about what is possible.

How to contact an app developer - Apple Support