I’m keeping it short. Add display icons that identify the mobility of actors / objects in the World Outliner. Also add abbreviated terms of the mobility of actors / objects to World Outliner. Example of abbreviated terms:
Stc, Stry, Mov
Use the icons that are already on the buttons for those settings in applicable actors / objects.
Then add the capability to organize / re-order things in the World Outliner based on the mobility. And make the icons / terms options to enable / disable in the World Outliner via Project Settings or Editor Preferences (that one is probably the most likely candidate).