In Blender 2.82a, on Ubuntu Studio 19.10, there would appear to be a place to add custom properties other than under the Object Data tab of the Properties Panel. Under the Tools tab of the Properties Shelf (N-Panel), there is seemingly another place to add them:
I am not clear on what adding them using this other method actually does, because I have found that, for any object currently selected which has had custom properties added via the Object Data tab, those custom properties cease being displayed in the Properties Panel as soon as that object is no longer selected (as one would expect, since the context has changed).
When custom properties are added via the Tools tab of the Properties Shelf, then unselecting the relevant object does not stop the custom properties from being displayed in the corresponding location of the Properties Shelf. Instead they remain visible. I am wondering why this is.
It would appear that adding the custom properties in these two ways is doing something different, and that these two approaches are not merely two different ways to do the same thing.