The ContentControl displays the object type name instead of rendering the DataTemplate after the ContentTemplateSelector has been set [WINUI]

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### Describe the bug

The ContentControl displays the object type name instead of rendering the DataTemplate after the ContentTemplateSelector has been set. The same implementation works as expected in WPF.

```
**MainWindow.xaml**

**MainWindow.xaml.cs
public sealed partial class MainWindow : Window
{
public Person MyPerson { get; set; } = new Person { Name = "John Doe" };
public MainWindow()
{
this.InitializeComponent();
stackPanel.DataContext = this;
}

private void Edit_Click(object sender, RoutedEventArgs e)
{
AppState.IsEditing = true;

MyContentControl.ContentTemplate = null;
MyContentControl.ContentTemplateSelector = (DataTemplateSelector)App.Current.Resources["MyTemplateSelector"];

var model = MyPerson;
MyContentControl.Content = null;
MyContentControl.Content = model;
}
}

**App.xaml**

**Person.cs**
public class Person
{
public string Name { get; set; }
}

**AppState.cs**
public static class AppState
{
public static bool IsEditing = false;
}

**MySelector.cs**
public class MySelector : DataTemplateSelector
{
public DataTemplate ViewTemplate { get; set; }
public DataTemplate EditTemplate { get; set; }

protected override DataTemplate SelectTemplateCore(object item, DependencyObject container)
{
return AppState.IsEditing ? EditTemplate : ViewTemplate;
}
}
```

### Steps to reproduce the bug

1. Run the sample
2. Click the "Enter Edit Mode" button.

**Observed Behavior**
The ContentControl displays the underlying object’s type name instead of rendering the expected DataTemplate provided by the ContentTemplateSelector.

### Expected behavior

When clicking the "Enter Edit Mode" button, the ContentControl should show the edit template instead of the object’s type name.

### Screenshots

### WinUI Demo Video ###

https://github.com/user-attachments/assets/6cc613ca-6e8d-4efa-aa1f-a44ba5d150a4

### WPF Demo Video ###

https://github.com/user-attachments/assets/8362de70-67c9-4da5-8102-3bb4bc03757b

### NuGet package version

WinUI 3 - Windows App SDK 1.7.2: 1.7.250513003

### Windows version

Windows 11 (24H2): Build 26100

### Additional context

_No response_

Start by running the provided MainWindow.xaml and MainWindow.xaml.cs sample with the App.xaml resources, Person.cs, AppState.cs, and MySelector.cs definitions on WinUI 3 / Windows App SDK 1.7.2. Reproduce the Enter Edit Mode action and trace ContentControl's template selection and content update behavior. Done means the edit DataTemplate renders instead of the Person type name after the selector is assigned.

Written by the indexing model from the issue text.