Integrate "Ignore for this session" better with config system

Because of the previous commit, this is needed to stop DolphinQt from
forgetting that the user pressed ignore whenever any part of the config
is changed.

This commit also changes the behavior a bit on DolphinQt: "Ignore for
this session" now applies to the current emulation session instead of
the current Dolphin launch. This matches how it already worked on
Android, and is in my opinion better because it means the user won't
lose out on important panic alerts in a game becase they played another
game first that had repeated panic alerts that they wanted to ignore.

For Android, this commit isn't necessary, but it makes the code cleaner.

Source/Core/DolphinQt/Main.cpp

@@ -92,7 +92,7 @@ static bool QtMsgAlertHandler(const char* caption, const char* text, bool yes_no
 
     if (button == QMessageBox::Ignore)
     {
-      Common::SetEnableAlert(false);
+      Config::SetCurrent(Config::MAIN_USE_PANIC_HANDLERS, false);
       return true;
     }