Cursor doesn't update after opening TimePicker and not moving mouse

### Describe the bug

When opening a TimePicker for the first time in an application's lifetime, the cursor will change to the busy cursor before the time picker flyout appears.

If you don't move the mouse after interacting with the TimePicker, the cursor will never change to the default cursor even after the flyout finishes loading.

### Steps to reproduce the bug

1. Place a `` inside a ``
2. Run the application
3. Click the time picker, while being careful to not move the mouse
4. Observe stuck busy cursor

### Expected behavior

The cursor should change back to the default cursor.

### Screenshots

_No response_

### NuGet package version

WinUI 3 - Windows App SDK 1.7.3: 1.7.250606001

### Windows version

Windows 11 (24H2): Build 26100

### Additional context

```xml

```

Start by reproducing the issue with the provided Window and TimePicker XAML on Windows 11, then trace the TimePicker flyout and cursor handling involved during its first opening. Done means the cursor returns to the default cursor after the flyout finishes loading without moving the mouse.

Written by the indexing model from the issue text.