Even though the interaction tab in the group settings states that Admin can see all groups, I am unable to have it visible in the list of groups that I can assign to a private category (in the 2nd screenshot). Only those that I am a member of appear. For that group to appear in the list, as Admin, I have to add myself as a member of that group. Is that the expected behavior?
The scenario here is that I was asked to create a private category, assign a group to it, but I do not want to be an explicit member of that group.