Does anyone have an idea like? How do I get Google home to mute my TV or receiver when talking to it? As I say “OK Google” that lowered the audio / video components?
Have you found a solution to this?
NO 
Interesting idea
I’d like this too (now that you’ve raised the possibility).
How about an alternative ‘listener’ where your TV is that only listens for ‘OK Google’ and then tells HA to mute the TV?
No need to say anything extra.
It must be out there!
The think is at the Ok Google, Google home not change state inside HA. So there is no way to capture this and mute the TV inside HA. I have done the mute think of Google home is playing something.