The app won't go to sleep

If I leave the Channels app open, it seems to prevent my iPad from going to sleep.
What setting do I need to change?

I assume you mean open but not playing anything?

Right.

There is no setting to change that that I am aware of. You may want to post in feature requests that you want the app to allow sleep if not actively playing video.

The app isn’t set to avoid sleep while open.

It is when video is playing. But the moment video is stopped or dismissed, the idle timer is turned back on.

Would you happen to be exiting the video player in some odd manner?

When a video is paused, but not fully exited from, does it count as “when video is playing”?

Yes, this counts as "playing". The video player being active (including having a stream on pause) will inhibit sleep.