[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"
/>

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## 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/ViewModels/ShellViewModel.cs

@@ -10,7 +10,9 @@ using System.Threading.Tasks;
 using System.Windows.Input;
 
 using Microsoft.PowerToys.Settings.UI.Helpers;
+using Microsoft.PowerToys.Settings.UI.Library;
 using Microsoft.PowerToys.Settings.UI.Library.Helpers;
+using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
 using Microsoft.PowerToys.Settings.UI.Services;
 using Microsoft.UI.Xaml.Controls;
 using Microsoft.UI.Xaml.Input;
@@ -26,31 +28,41 @@ namespace Microsoft.PowerToys.Settings.UI.ViewModels
         private readonly KeyboardAccelerator backKeyboardAccelerator = BuildKeyboardAccelerator(VirtualKey.GoBack);
 
         private bool isBackEnabled;
+        private bool showCloseMenu;
         private IList<KeyboardAccelerator> keyboardAccelerators;
         private NavigationView navigationView;
         private NavigationViewItem selected;
         private ICommand loadedCommand;
         private ICommand itemInvokedCommand;
         private NavigationViewItem[] _fullListOfNavViewItems;
+        private GeneralSettings _generalSettingsConfig;
 
         public bool IsBackEnabled
         {
-            get { return isBackEnabled; }
-            set { Set(ref isBackEnabled, value); }
+            get => isBackEnabled;
+            set => Set(ref isBackEnabled, value);
+        }
+
+        public bool ShowCloseMenu
+        {
+            get => showCloseMenu;
+            set => Set(ref showCloseMenu, value);
         }
 
         public NavigationViewItem Selected
         {
-            get { return selected; }
-            set { Set(ref selected, value); }
+            get => selected;
+            set => Set(ref selected, value);
         }
 
         public ICommand LoadedCommand => loadedCommand ?? (loadedCommand = new RelayCommand(OnLoaded));
 
         public ICommand ItemInvokedCommand => itemInvokedCommand ?? (itemInvokedCommand = new RelayCommand<NavigationViewItemInvokedEventArgs>(OnItemInvoked));
 
-        public ShellViewModel()
+        public ShellViewModel(ISettingsRepository<GeneralSettings> settingsRepository)
         {
+            _generalSettingsConfig = settingsRepository.SettingsConfig;
+            ShowCloseMenu = !_generalSettingsConfig.ShowSysTrayIcon;
         }
 
         public void Initialize(Frame frame, NavigationView navigationView, IList<KeyboardAccelerator> keyboardAccelerators)