Update hardcore toggle to use rc_client

The client can take care of itself and handle its own hardcore status when it toggles, so I can tell the settings widget to contact the manager directly to set it.
Also, gradually reorganizing the settings dialog over the next handful of commits.

Source/Core/Core/AchievementManager.h

@@ -103,6 +103,7 @@ public:
   void DoFrame();
 
   std::recursive_mutex& GetLock();
+  void SetHardcoreMode();
   bool IsHardcoreModeActive() const;
   std::string_view GetPlayerDisplayName() const;
   u32 GetPlayerScore() const;