A neater way to implement this would be to create a new RecentObjects class accessible from the DisplayState class.
It would need a methods to add a new object to a list and retrieve an object list, and also methods to load and save the json file. Your json file format looks reasonable.
The class should also monitor the object deleted signals so that deleted objects can be removed from the lists. It could also monitor other signals if required.
We could then use recent objects for other purposes. Perhaps we could also consider using it to populate the “Go” menu?