TitleBar with IconSource resets the mouse cursor to the arrow on every layout pass

### Describe the bug

When a `TitleBar` has `IconSource` set (and is used as the window title bar through `ExtendsContentIntoTitleBar` + `SetTitleBar`), the mouse cursor is reset to the default arrow whenever a layout pass happens anywhere in the window while the pointer is not moving.

This affects every cursor in the window: the I-beam of a `TextBox`, cursors set with `UIElement.ProtectedCursor`, etc. The correct cursor comes back only when the mouse is physically moved, so any UI that updates continuously (data bindings, a live image, `ScrollView` animations) shows the arrow most of the time while the pointer rests on it.

Without `IconSource`, the cursor behaves correctly.

### Why is this important?

Setting `TitleBar.IconSource`, the standard way to show the app icon, breaks the mouse cursor in the whole window: any UI that updates (bindings, live images, scroll animations) resets `TextBox` I-beams and custom `ProtectedCursor` cursors to the arrow. App code can't restore the cursor until the mouse moves, and the cause is very hard to trace.

### Steps to reproduce the bug

1. Create an unpackaged WinUI 3 app with this `MainWindow`:

```xml

```

```csharp
public sealed partial class MainWindow : Window
{
private readonly DispatcherTimer _timer = new() { Interval = TimeSpan.FromMilliseconds(500) };
private int _updates;

public MainWindow()
{
InitializeComponent();

ExtendsContentIntoTitleBar = true;
SetTitleBar(AppTitleBar);

// Any layout pass triggers the cursor reset: a changing text is enough
_timer.Tick += (_, _) => ChangingText.Text = $"Text update #{++_updates}";
_timer.Start();
}

private void OnIconSourceCheckBoxClick(object sender, RoutedEventArgs e) =>
AppTitleBar.IconSource = IconSourceCheckBox.IsChecked == true ? new FontIconSource { Glyph = "" } : null;
}
```

2. Run the app, move the pointer over the `TextBox` and then keep the mouse still.
3. Observe the cursor at every text update (every 0.5 s).
4. Uncheck "TitleBar.IconSource set" and repeat step 2.

### Actual behavior

With `IconSource` set, the cursor turns into the arrow at every text update and stays so until the mouse is moved. With `IconSource` cleared (step 4), the cursor stays the I-beam.

Setting the cursor again from the app does not help: once reset, the displayed cursor does not change with `ProtectedCursor`, `InputPointerSource.Cursor` or Win32 `SetCursor` until a real mouse move.

### Expected behavior

The cursor stays the I-beam while the pointer rests on the `TextBox`, whatever happens elsewhere in the window.

### Screenshots

_No response_

### NuGet package version

Windows App SDK 2.5.1 (also reproduced with 2.2.0).

### Windows version

Windows 11 (25H2): Build 26200

### Additional context

[CursorRepro.zip](https://github.com/user-attachments/files/32392465/CursorRepro.zip)

Start with the MainWindow repro in the attached CursorRepro.zip, especially the TitleBar.IconSource, SetTitleBar, and DispatcherTimer setup. Trace the layout and cursor behavior with IconSource enabled and disabled; done means the TextBox keeps its I-beam and other custom cursors during layout updates without mouse movement.

Written by the indexing model from the issue text.