So after walking away from the problem for a bit and making some coffee, I started combing through the .ini files. I eventually found a setting in the ServerSettings.ini file called “BuildingPickupEnabled” it was set to false. Once I changed it to true, everything worked as it should. The restored game from backup also worked, once the setting was set to true.
I have no idea what changed it, but now I know where to look if the problem comes up again. I hope this helps others who are dealing with the same, or similar issue.