Use case is right on! However the switching from Instagram dropdown doesn’t seem to work. Firstly, the hierarchies are different, meaning if you have a dropdown besides Instagram, it could only change those products, maybe Facebook, WhatsApp, and so on. It cannot change the user profile/group. That will fall in the next level, thus underneath where the profile icon is.
Secondly, because of that, the feedback as to which group has been is absent. No visual indication is present In my opinion, it is imperative to show which group is being viewed as it controls the entire content below.
Thus the dropdown option is a bit dicy. Things around the user’s display picture where presently stories are added, or the home icon as you suggested, or even the profile icon could work.
Also, interesting to know why you chose the word ‘groups’. You were already talking about feeds, which could be a better match!