Sanity check on WPF CustomControl Binding to ViewModel not working

public class MyViewModel : INotifyPropertyChanged {
  public event PropertyChangedEventHandler? PropertyChanged;
  private string _selectedText;
  public string SelectedText { 
    get => _selectedText; 
    set { _selectedText = value; PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(nameof(SelectedText))); }
  }
}

public class AlertTextBox: RichTextBox {
  public static readonly DependencyProperty SelectedTextProperty = DependencyProperty.Register(nameof(SelectedText), typeof(string), typeof(AlertTextBox));
  public string SelectedText
  {
    get => (string)GetValue(SelectedTextProperty);
    set => SetValue(SelectedTextProperty, value);
  }
  public AlertTextBox(){
    Selection.Changed += SelectionChanged;
  }
  public void SelectionChanged(object sender, EventArgs e) => SetCurrentValue(SelectedTextProperty, Selection.Text);
}

   <AlertTextBox SelectedText="{Binding Path=SelectedText}" />