citra_qt/main: Save settings when starting guest

Saves UISettings and Settings when booting a guest. Moves updating
UISettings::values from GMainWindow::closeEvent into its own function,
then reuses it in GMainWindow::BootGame.

Co-Authored-By: lat9nq <22451773+lat9nq@users.noreply.github.com>

src/citra_qt/main.h

@@ -229,6 +229,7 @@ private:
     void UpdateStatusBar();
     void LoadTranslation();
     void UpdateWindowTitle();
+    void UpdateUISettings();
     void RetranslateStatusBar();
     void InstallCIA(QStringList filepaths);
     void HideMouseCursor();