[PowerToys Run] Implemented Setting to Clear Search Query when PowerToys Run is Launched (#4995)

* Implemented Clear Input On Launch

* Move logic to seperate command on viewmodel

* Added Settings Sync
Moved logic from OnDeactivated to OnActivated

* Complete after testing

Co-authored-by: Roy <royvou@hotmailcom>

src/core/Microsoft.PowerToys.Settings.UnitTest/ViewModelTests/PowerLauncherViewModelTest.cs

@@ -131,5 +131,7 @@ namespace ViewModelTests
             Assert.IsTrue(mockSettings.properties.override_win_r_key);
             Assert.IsFalse(mockSettings.properties.override_win_s_key);
         }
+
+
     }
 }