Those examples look like a good explanation of plugins. To Unreal Build Tool, plugins are really just modules that cannot be linked to from game modules, so they add functionality without needing any communication from the game.
I think if you want to be calling your module’s functions from inside your game, it’ll need to be a module. You should be able to do this by just creating a new sub-folder underneath your game’s Source folder with an associated .Build.cs file.
If you have the VehicleGame sample project, its loading screen is implemented as a separate module. You can see it has a public VehicleGameLoadingScreen.h header which is included from the main VehicleGame module which is called from inside AVehicleHUD_Menu::ShowLoadingScreen().
Hopefully that gives you something to look at 