I have exact same problem. HomePod does not work streaming from iTunes with AppleTV also being used for Whole house audio. Here is what works, when I use the exact same settings, Sonos speaker and Apple TV stream fine using Airplay 2 from iTunes on a Mac Pro. Also, when I use iTunes with HomePod as well as AppleTV, Airfoil has absolutely no dropouts when I do not use the Airplay in iTunes and just use Airfoil to stream iTunes app to all speakers in my house (9). This has been a massive problem since iOS 13. Apple have not fixed it. Use Airfoil to stream, or buy a properly working Sonos speaker that does not drop audio anywhere. The HomePod does not work with multiple items playing in iTunes/Music. If you stream from phone only to one HomePod, you might be OK. That is pretty bad for a $270 speaker. I have it on good authority the HomePod Mini is just as bad at streaming in the same situation. Apple don't care.