I thought I would mention that I have found a temporary workaround for certain use cases only, but one that only works if your phone is out (not in your pocket or something). The workaround is to change the settings in Assistant to NOT listen through BT. It will at least hear your voice through your phone mic and respond - again if your phone is out. I tested this on my BT headset and in my car BT and was able to replicate it.
Obviously this is of no help to someone with their phone in their pocket tapping their headset and trying to talk to Assistant, but it is a help for me for example, when I am connected to my car BT and I can say "OK Google, navigate Home" again - with my phone out to hear me.
It's deep in the settings if you want to try it .
Assistant --> (top right) Menu --> Overflow menu (...) --> Settings --> (under "Devices") "Phone" --> Other Voice Settings --> Bluetooth Headset (Toggle OFF)