feat(ui): worker-menu Shutdown ends worker + app after confirm

Adds a Shutdown entry after the Worker menu's Restart/Update Claude CLI
items. Confirms via IDialogService.ConfirmAsync, then kills this
installation's ClaudeDo.Worker process(es) (shared kill loop, extracted
from RestartWorkerService) and force-closes the window through the same
_forceClose path MainWindow already uses for the Mission-Control close
confirm, so no second confirmation dialog shows.

src/ClaudeDo.Ui/ViewModels/IslandsShellViewModel.cs

@@ -658,8 +658,17 @@ public sealed partial class IslandsShellViewModel : ViewModelBase, IDisposable
         var exe = _workerLocator.Find();
         if (exe is null) throw new InvalidOperationException("Worker executable not found.");
 
-        // Only kill the worker belonging to THIS installation — not any other
-        // ClaudeDo.Worker on the machine (e.g. a second install).
+        KillMatchingWorkerProcesses(exe);
+
+        var started = System.Diagnostics.Process.Start(new System.Diagnostics.ProcessStartInfo(exe) { UseShellExecute = true });
+        if (started is not null && started.WaitForExit(RestartSurvivalCheckMs))
+            throw new InvalidOperationException($"worker process exited immediately (code {started.ExitCode})");
+    }
+
+    // Only kill the worker belonging to THIS installation — not any other
+    // ClaudeDo.Worker on the machine (e.g. a second install).
+    private static void KillMatchingWorkerProcesses(string exe)
+    {
         var exeFull = System.IO.Path.GetFullPath(exe);
         foreach (var p in System.Diagnostics.Process.GetProcessesByName("ClaudeDo.Worker"))
         {
@@ -675,10 +684,29 @@ public sealed partial class IslandsShellViewModel : ViewModelBase, IDisposable
             catch { /* may have exited or be inaccessible */ }
             finally { p.Dispose(); }
         }
+    }
 
-        var started = System.Diagnostics.Process.Start(new System.Diagnostics.ProcessStartInfo(exe) { UseShellExecute = true });
-        if (started is not null && started.WaitForExit(RestartSurvivalCheckMs))
-            throw new InvalidOperationException($"worker process exited immediately (code {started.ExitCode})");
+    // Set by MainWindow: force-closes the window without re-triggering its own close
+    // confirmation (the shutdown dialog above already confirmed).
+    public Action? CloseWindow { get; set; }
+
+    // Test seam: overrides the real kill-worker + close-window body.
+    internal Action? ShutdownOperation { get; set; }
+
+    [RelayCommand]
+    private async Task ShutdownAsync()
+    {
+        if (Dialogs is null) return;
+        var confirmed = await Dialogs.ConfirmAsync(Loc.T("vm.shell.shutdownConfirm"));
+        if (!confirmed) return;
+        (ShutdownOperation ?? ShutdownWorkerAndCloseApp)();
+    }
+
+    private void ShutdownWorkerAndCloseApp()
+    {
+        var exe = _workerLocator.Find();
+        if (exe is not null) KillMatchingWorkerProcesses(exe);
+        CloseWindow?.Invoke();
     }
 
     private bool _updatingClaudeCli;

src/ClaudeDo.Ui/Views/MainWindow.axaml

@@ -68,6 +68,9 @@
                         Command="{Binding OpenUsageMonitorCommand}"/>
               <MenuItem Header="{loc:Tr shell.menu.updateClaudeCli}"
                         Command="{Binding UpdateClaudeCliCommand}"/>
+              <Separator/>
+              <MenuItem Header="{loc:Tr shell.menu.shutdown}"
+                        Command="{Binding ShutdownCommand}"/>
             </MenuItem>
             <MenuItem Header="{loc:Tr shell.menu.repositories}"
                       FontSize="{StaticResource FontSizeMono}"

src/ClaudeDo.Ui/Views/MainWindow.axaml.cs

@@ -80,6 +80,11 @@ public partial class MainWindow : Window
                     WindowState = WindowState.Normal;
                 Activate();
             };
+            vm.CloseWindow = () =>
+            {
+                _forceClose = true;
+                Close();
+            };
             if (vm.Tasks is not null)
                 vm.Tasks.IsWindowVisible = WindowState != WindowState.Minimized;
         }