Previous discussion here: Apple TV + Channels + HomePods
Does disabling Picture in Picture help the situation for you? It did for me.
I have one AppleTV 4K on my kitchen TV that is set to send audio out by default to one HomePod mini. I started to experience consistent issues last year, specifically when starting any live show or recording, the playback would immediately pause, and I had to FF or exit and re-enter to get everything playing as expected.
Just wanted to report that as of today, with that AppleTV on the latest tvOS public beta (17.3,) Channels DVR on the latest prerelease, the Channels client on the latest TestFlight, with "Lab" selected in Channels' Settings > Playback > Advanced > Audio, I'm not experiencing those issues any more. It's working much better. Hopefully this will be fixable for everyone else out there too and that invoking PIP won't impact it negatively.