Groups are borderline impossible because you have API access only to the groups you are admin of. So of no use to spy on any other group, even if it’s public.
A related question.
I am the admin of some groups which are technically not my group. I am assisting someone else.
Would the tool still be useful for figuring out what people are doing or other insight? Yes, I am very new to the solution so not really up to speed on what it is best at.
Is there a way to create an extension (Chromium, Firefox, Chrome, etc.) that could mimic this behavior browser-side?
Yes, one of the solutions to get group data / user insights in groups is to make an extension that can crawl the given groups.
We are not interested in this approach because it violates the facebook tos - but i’m sure these kind of grey-hat tools exist out there.