Have been experiencing this same issue. Glad to see that there seems to be some work arounds! Thanks everyone for sharing.
Possible short term in-the-moment solution: In reading this post I ended up unplugging then plugging back in the Brio webcam and this seemed to resolve the issue (at least for now). If this problem comes back for anyone in the middle of a meeting I would suggest doing this to hopefully resolve it for that meeting.
In past meetings I basically had to revert to muting my mic and only using the chat to communicate, and in some of those meetings I was leading/presenting something. So frustrating!
Also for anyone else troubleshooting this, for the longest time I couldn't figure out what was going on or how to test it because I couldn't hear the audio loop but everyone else on the call could. I realized that if you go to the Zoom audio settings and test out the mic you can hear the audio loop. You can also go to your Mac sound input settings and see that it is picking up audio (the loop) even though there are no sounds in your environment. Once I unplugged and plugged the Brio back in, I could see that the loop was gone through both of those methods.