feat(ui): prompt once on worker connection failure with grace timer

Adds ShowWorkerConnectionModal hook, DecideShowConnectionPrompt one-shot gate, OpenWorkerConnectionHelp relay command, and a 12 s _connectTimer to IslandsShellViewModel; covered by two new unit tests.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/ClaudeDo.Ui/ViewModels/IslandsShellViewModel.cs

@@ -51,6 +51,9 @@ public sealed partial class IslandsShellViewModel : ViewModelBase
     // Set by MainWindow to open the global worktrees overview dialog.
     public Func<WorktreesOverviewModalViewModel, Task>? ShowWorktreesOverviewModal { get; set; }
 
+    // Set by MainWindow to open the worker-connection help dialog.
+    public Func<WorkerConnectionModalViewModel, Task>? ShowWorkerConnectionModal { get; set; }
+
     [ObservableProperty] private bool _isUpdateBannerVisible;
     [ObservableProperty] private string? _updateBannerLatestVersion;
     [ObservableProperty] private string? _inlineUpdateStatus;
@@ -72,6 +75,7 @@ public sealed partial class IslandsShellViewModel : ViewModelBase
     public bool ShowLists => WindowWidth >= 780;
 
     private readonly System.Timers.Timer _clearTimer = new(30_000) { AutoReset = false };
+    private readonly System.Timers.Timer _connectTimer = new(12_000) { AutoReset = false };
 
     [ObservableProperty] private string? _primeStatus;
     private readonly System.Timers.Timer _primeStatusTimer = new(5_000) { AutoReset = false };
@@ -220,6 +224,11 @@ public sealed partial class IslandsShellViewModel : ViewModelBase
         };
         _primeStatusTimer.Elapsed += (_, _) =>
             Avalonia.Threading.Dispatcher.UIThread.Post(() => PrimeStatus = null);
+        _connectTimer.Elapsed += (_, _) => Dispatcher.UIThread.Post(() =>
+        {
+            if (DecideShowConnectionPrompt(IsOffline)) _ = OpenWorkerConnectionHelpAsync();
+        });
+        _connectTimer.Start();
         _ = Lists.LoadAsync();
         _updateCheck.PropertyChanged += (_, e) =>
         {
@@ -269,6 +278,25 @@ public sealed partial class IslandsShellViewModel : ViewModelBase
         if (ShowAboutModal is not null) await ShowAboutModal(vm);
     }
 
+    private bool _connectionPromptShown;
+
+    internal bool DecideShowConnectionPrompt(bool isOffline)
+    {
+        if (!isOffline) return false;
+        if (_connectionPromptShown) return false;
+        _connectionPromptShown = true;
+        return true;
+    }
+
+    private async Task OpenWorkerConnectionHelpAsync()
+    {
+        var vm = new WorkerConnectionModalViewModel(_workerLocator, _installerLocator);
+        if (ShowWorkerConnectionModal is not null) await ShowWorkerConnectionModal(vm);
+    }
+
+    [RelayCommand]
+    private Task OpenWorkerConnectionHelp() => OpenWorkerConnectionHelpAsync();
+
     [RelayCommand]
     private async Task OpenRepoImport()
     {

tests/ClaudeDo.Ui.Tests/ConnectionPromptGateTests.cs

@@ -0,0 +1,22 @@
+using ClaudeDo.Ui.ViewModels;
+using Xunit;
+
+namespace ClaudeDo.Ui.Tests;
+
+public class ConnectionPromptGateTests
+{
+    [Fact]
+    public void Shows_once_when_offline()
+    {
+        var vm = new IslandsShellViewModel();
+        Assert.True(vm.DecideShowConnectionPrompt(isOffline: true));
+        Assert.False(vm.DecideShowConnectionPrompt(isOffline: true)); // not a second time
+    }
+
+    [Fact]
+    public void Does_not_show_when_connected_before_grace()
+    {
+        var vm = new IslandsShellViewModel();
+        Assert.False(vm.DecideShowConnectionPrompt(isOffline: false));
+    }
+}