[Settings] Move title bar shutdown button to navigation view (#40714)

<!-- Enter a brief description/summary of your PR here. What does it
fix/what does it change/how was it tested (even manually, if necessary)?
-->
## Summary of the Pull Request

Based on
https://github.com/microsoft/PowerToys/pull/40260#issuecomment-3085099815
feedback, this PR remove the title bar shutdown button in favor of a
menu item in the navigation view footer.

- Menu item is visible only when tray icon is hidden
- A confirm dialog has been added

<img width="848" height="448" alt="image"
src="https://github.com/user-attachments/assets/529bcfa9-94ed-48b1-b2bb-ca6993d12e0f"
/>

<img width="848" height="448" alt="image"
src="https://github.com/user-attachments/assets/febafbb4-3a5b-4b04-8065-28f0d269ab6c"
/>

- Close is used in tray icon menu for closing app

<img alt="image"
src="https://github.com/user-attachments/assets/3ac79a8c-961f-4f95-8967-adef00aba77b"
/>

<img alt="image"
src="https://github.com/user-attachments/assets/c2800a77-c733-41a9-aa4f-fa4c2afd30a3"
/>

<!-- Please review the items on the PR checklist before submitting-->
## PR Checklist

- [x] **Closes:** #40346 #40577
- [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
- [x] **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

<!-- Provide a more detailed description of the PR, other things fixed,
or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed

- Open settings with tray icon visible: close menu is hidden
- Open settings with tray icon hidden: close menu is visible
- Tested close menu visibility change when tray icon option is changed
- Tested cancel button of close dialog
- Tested close button of dialog

---------

Co-authored-by: Niels Laute <niels.laute@live.nl>

src/settings-ui/Settings.UI/SettingsXAML/Views/GeneralPage.xaml.cs

@@ -10,7 +10,6 @@ using Microsoft.PowerToys.Settings.UI.Flyout;
 using Microsoft.PowerToys.Settings.UI.Helpers;
 using Microsoft.PowerToys.Settings.UI.Library;
 using Microsoft.PowerToys.Settings.UI.ViewModels;
-using Microsoft.UI.Dispatching;
 using Microsoft.UI.Xaml;
 using Microsoft.UI.Xaml.Controls;
 using Windows.Data.Json;
@@ -174,19 +173,6 @@ namespace Microsoft.PowerToys.Settings.UI.Views
             await Task.Run(ViewModel.ViewDiagnosticData);
         }
 
-        private void ExitPTItem_Tapped(object sender, RoutedEventArgs e)
-        {
-            const string ptTrayIconWindowClass = "PToyTrayIconWindow"; // Defined in runner/tray_icon.h
-            const nuint ID_EXIT_MENU_COMMAND = 40001;                  // Generated resource from runner/runner.base.rc
-
-            // Exit the XAML application
-            Application.Current.Exit();
-
-            // Invoke the exit command from the tray icon
-            IntPtr hWnd = NativeMethods.FindWindow(ptTrayIconWindowClass, ptTrayIconWindowClass);
-            NativeMethods.SendMessage(hWnd, NativeMethods.WM_COMMAND, ID_EXIT_MENU_COMMAND, 0);
-        }
-
         private void BugReportToolClicked(object sender, RoutedEventArgs e)
         {
             // Start bug report
@@ -232,5 +218,17 @@ namespace Microsoft.PowerToys.Settings.UI.Views
                 ShellPage.ShellHandler.IPCResponseHandleList.Remove(HandleBugReportStatusResponse);
             }
         }
+
+        private void ShowSystemTrayIcon_Toggled(object sender, RoutedEventArgs e)
+        {
+            if (sender is ToggleSwitch toggleSwitch)
+            {
+                var shellViewModel = ShellPage.ShellHandler?.ViewModel;
+                if (shellViewModel != null)
+                {
+                    shellViewModel.ShowCloseMenu = !toggleSwitch.IsOn;
+                }
+            }
+        }
     }
 }