The functionality of rearranging entries individually is not present in: Selection Sets, FlexTables, Profiles, Queries, Scenarios (on the same level), Alternatives (on the same level) and probably a few that I'm missing. For some of these there is a workaround, for example for Flextables it is possible to rearrange by moving the Flextable to another folder and moving it back, thereby adding the Flextable to the bottom of a folder, but it is not very convenient.

The functionality is present in e.g. Element Symbology and Background Layers. These can be used as examples of how it could be implemented.