ControllerInterface: Make the ID assigning code common

This makes the device ID assigning code common to all backends, by
moving it to AddDevice() instead of copy-pasting or replicating
the logic in the backends.

Also, to prepare for hotplugging, instead of relying on a name usage
count, the new ID assigning system always starts from ID 0 and tries
to assign the first ID that is not used.

Source/Core/InputCommon/ControllerInterface/DInput/DInputKeyboardMouse.h

@@ -89,7 +89,6 @@ public:
   ~KeyboardMouse();
 
   std::string GetName() const override;
-  int GetId() const override;
   std::string GetSource() const override;
 
 private: