An umbrella personality encompasses a larger group than would be normal. Instead of feeling a strong bond only to the people closest to you, with an umbrella personality this feeling widens to enclose all the people in the respective group.
"(..) its members developed feelings of friendship not only for one another but also for the group itself"
in your post is the exact description of what an umbrella personality is
I'm not sure if this can be translated with "geschützer Raum". Is "geschützter Raum" a German phrase I'm not aware of?
Are you using "geschützter Raum" to mean "safe harbour" or something similar? Because this is something different.
Perhaps saying something like "vergrößertes/verstärktes Gruppenzugehörigkeitsgefühl" might help you? Help from German native speakers please! :)