move Automation Notification functionality to UIHelper, implement UIHelper in ListPage and SettingsWindow (#41016)

## Summary of the Pull Request
Fixed #41014 and it overlapped with #40761, so I made a UIHelper
patterning off of WinUI Gallery's
[UIHelpder](0576fb508a/WinUIGallery/Helpers/UIHelper.cs (L63))

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## PR Checklist

- [x] Closes: #41014
- [x] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
- [ ] [JSON for
signing](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ESRPSigning_core.json)
for new binaries
- [ ] [WXS for
installer](https://github.com/microsoft/PowerToys/blob/main/installer/PowerToysSetup/Product.wxs)
for new binaries and localization folder
- [ ] [YML for CI
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
for new test projects
- [ ] [YML for signed
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/release.yml)
- [ ] **Documentation updated:** If checked, please file a pull request
on [our docs
repo](https://github.com/MicrosoftDocs/windows-uwp/tree/docs/hub/powertoys)
and link it here: #xxx

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or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

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https://github.com/user-attachments/assets/011ee8c1-baaf-47fc-b8f8-ee489b01702b

src/modules/cmdpal/Microsoft.CmdPal.UI/Settings/SettingsWindow.xaml.cs

@@ -10,6 +10,7 @@ using Microsoft.CmdPal.UI.ViewModels;
 using Microsoft.CmdPal.UI.ViewModels.Messages;
 using Microsoft.UI.Windowing;
 using Microsoft.UI.Xaml;
+using Microsoft.UI.Xaml.Automation.Peers;
 using Microsoft.UI.Xaml.Controls;
 using WinUIEx;
 using RS_ = Microsoft.CmdPal.UI.Helpers.ResourceLoaderInstance;
@@ -22,6 +23,9 @@ public sealed partial class SettingsWindow : WindowEx,
 {
     public ObservableCollection<Crumb> BreadCrumbs { get; } = [];
 
+    // Gets or sets optional action invoked after NavigationView is loaded.
+    public Action NavigationViewLoaded { get; set; } = () => { };
+
     public SettingsWindow()
     {
         this.InitializeComponent();
@@ -35,10 +39,33 @@ public sealed partial class SettingsWindow : WindowEx,
         WeakReferenceMessenger.Default.Register<QuitMessage>(this);
     }
 
+    // Handles NavigationView loaded event.
+    // Sets up initial navigation and accessibility notifications.
     private void NavView_Loaded(object sender, RoutedEventArgs e)
     {
+        // Delay necessary to ensure NavigationView visual state can match navigation
+        Task.Delay(500).ContinueWith(_ => this.NavigationViewLoaded?.Invoke(), TaskScheduler.FromCurrentSynchronizationContext());
+
         NavView.SelectedItem = NavView.MenuItems[0];
         Navigate("General");
+
+        if (sender is NavigationView navigationView)
+        {
+            // Register for pane open/close changes to announce to screen readers
+            navigationView.RegisterPropertyChangedCallback(NavigationView.IsPaneOpenProperty, AnnounceNavigationPaneStateChanged);
+        }
+    }
+
+    // Announces navigation pane open/close state to screen readers for accessibility.
+    private void AnnounceNavigationPaneStateChanged(DependencyObject sender, DependencyProperty dp)
+    {
+        if (sender is NavigationView navigationView)
+        {
+            UIHelper.AnnounceActionForAccessibility(
+            ue: (UIElement)sender,
+            (sender as NavigationView)?.IsPaneOpen == true ? RS_.GetString("NavigationPaneOpened") : RS_.GetString("NavigationPaneClosed"),
+            "NavigationViewPaneIsOpenChangeNotificationId");
+        }
     }
 
     private void NavView_ItemInvoked(NavigationView sender, NavigationViewItemInvokedEventArgs args)
@@ -109,24 +136,15 @@ public sealed partial class SettingsWindow : WindowEx,
         WeakReferenceMessenger.Default.UnregisterAll(this);
     }
 
-    private void PaneToggleBtn_Click(object sender, RoutedEventArgs e)
-    {
-        NavView.IsPaneOpen = !NavView.IsPaneOpen;
-    }
-
     private void NavView_DisplayModeChanged(NavigationView sender, NavigationViewDisplayModeChangedEventArgs args)
     {
         if (args.DisplayMode == NavigationViewDisplayMode.Compact || args.DisplayMode == NavigationViewDisplayMode.Minimal)
         {
-            PaneToggleBtn.Visibility = Visibility.Visible;
             NavView.IsPaneToggleButtonVisible = false;
-            AppTitleBar.Margin = new Thickness(48, 0, 0, 0);
         }
         else
         {
-            PaneToggleBtn.Visibility = Visibility.Collapsed;
             NavView.IsPaneToggleButtonVisible = true;
-            AppTitleBar.Margin = new Thickness(16, 0, 0, 0);
         }
     }