Open apps should show the Space Name and Type somewhere. I personally would want to see the Space badge (blue for shared, red for managed) shown directly next to the app name. See my attached mock up. I typically know what spaces my apps live in but I'm always unsure if i'm in shared vs managed.
“Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.” — Antoine de Saint-Exupéry