CmdPal: Add hidden window as owner for tool windows (#42902)

## Summary of the Pull Request

This PR changes the method used to hide tool windows from the taskbar
and Alt+Tab to a more reliable approach.
Previously, this was achieved by adding `WS_EX_TOOLWINDOW` to an unowned
top-level window, which proved unreliable in several scenarios.

The new implementation assigns a hidden window as the owner of each tool
window.
This ensures that the window does not appear on the taskbar even when
the Windows setting
**Settings → System → Multitasking → On the taskbar, show all opened
windows** is set to **On all desktops**.

## Change log one-liner

Fixes Command Palette windows occasionally appearing on the taskbar
under certain system settings.

<!-- Please review the items on the PR checklist before submitting-->
## PR Checklist

- [x] Closes: #42395
- [x] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [x] **Tests:** Added/updated and all pass
- [x] **Localization:** All end-user-facing strings can be localized
- [x] **Dev docs:** Added/updated
- [x] **New binaries:** none
- [x] **Documentation updated:** no need

<!-- Provide a more detailed description of the PR, other things fixed,
or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

Tested alongside the stable CmdPal on a system with

src/modules/cmdpal/Microsoft.CmdPal.UI/MainWindow.xaml.cs

@@ -57,6 +57,7 @@ public sealed partial class MainWindow : WindowEx,
     private readonly List<TopLevelHotkey> _hotkeys = [];
     private readonly KeyboardListener _keyboardListener;
     private readonly LocalKeyboardListener _localKeyboardListener;
+    private readonly HiddenOwnerWindowBehavior _hiddenOwnerBehavior = new();
     private bool _ignoreHotKeyWhenFullScreen = true;
 
     private DesktopAcrylicController? _acrylicController;
@@ -65,6 +66,7 @@ public sealed partial class MainWindow : WindowEx,
     public MainWindow()
     {
         InitializeComponent();
+        HideWindow();
 
         _hwnd = new HWND(WinRT.Interop.WindowNative.GetWindowHandle(this).ToInt32());
 
@@ -73,6 +75,8 @@ public sealed partial class MainWindow : WindowEx,
             CommandPaletteHost.SetHostHwnd((ulong)_hwnd.Value);
         }
 
+        _hiddenOwnerBehavior.ShowInTaskbar(this, Debugger.IsAttached);
+
         _keyboardListener = new KeyboardListener();
         _keyboardListener.Start();
 
@@ -126,16 +130,6 @@ public sealed partial class MainWindow : WindowEx,
 
         // Force window to be created, and then cloaked. This will offset initial animation when the window is shown.
         HideWindow();
-
-        ApplyWindowStyle();
-    }
-
-    private void ApplyWindowStyle()
-    {
-        // Tool windows don't show up in ALT+TAB, and don't show up in the taskbar
-        // Since tool windows have smaller corner radii, we need to force the normal ones
-        this.ToggleExtendedWindowStyle(WINDOW_EX_STYLE.WS_EX_TOOLWINDOW, !Debugger.IsAttached);
-        this.SetCornerPreference(DWM_WINDOW_CORNER_PREFERENCE.DWMWCP_ROUND);
     }
 
     private static void LocalKeyboardListener_OnKeyPressed(object? sender, LocalKeyboardListenerKeyPressedEventArgs e)
@@ -264,7 +258,7 @@ public sealed partial class MainWindow : WindowEx,
         // because that would make it hard to debug the app
         if (Debugger.IsAttached)
         {
-            ApplyWindowStyle();
+            _hiddenOwnerBehavior.ShowInTaskbar(this, true);
         }
 
         // Just to be sure, SHOW our hwnd.