Try booting the phone in safe mode to ensure it's not a third party app?
Thanks for the suggestion. I put phone into safe mode. No help.
Repeat with possibly a bit more clarity:
If car has Bluetooth device selected, then when I activate Google Assistant and ask to send a text message, I do get the audio feedback: to whom, what's the message, etc. So this is how it works in safe or normal mode, and this is how you want it to work.
But if I'm listening to radio and try to interact with Assistant using audio, there is no spoken feedback, neither on the car system or the phone itself. Also when I press the microphone on my phone to speak, it does not silence the radio.
Now maybe this is all a car system can do with Bluetooth Audio/Music, but it certainly behaves better with Bluetooth Phone: in that case the radio is silenced, whether for incoming or outgoing call.
I'm inclined to call this a bug in the Hondalink audio system.