Fix MainWindow visibility logic:

- Restore Hide() method in MainViewModel (accidentally deleted)
- Fix Show() method which was incorrectly calling HideRequested
- Ensure OpenSettings cleanly hides MainWindow before showing SettingsWindow

Flow.Launcher.Avalonia/ViewModel/MainViewModel.cs

@@ -208,6 +208,19 @@ public partial class MainViewModel : ObservableObject
         }
     }
 
+    /// <summary>
+    /// Hide the main window.
+    /// </summary>
+    public void Hide()
+    {
+        MainWindowVisibility = false;
+        QueryText = "";
+        ActiveView = ActiveView.Results;
+        ContextMenu.Clear();
+        HideRequested?.Invoke();
+        Log.Info(ClassName, "Hide requested");
+    }
+
     /// <summary>
     /// Show the main window.
     /// </summary>
@@ -217,8 +230,8 @@ public partial class MainViewModel : ObservableObject
         QueryText = "";
         ActiveView = ActiveView.Results;
         ContextMenu.Clear();
-        HideRequested?.Invoke();
+        ShowRequested?.Invoke();
-        Log.Info(ClassName, "Hide requested");
+        Log.Info(ClassName, "Show requested");
     }
 
     /// <summary>