feat(ui): add reconcile tick to self-heal lost worker broadcasts

TasksIslandViewModel now runs a periodic tick that diffs the flat Items
collection against SQLite and patches properties in place (capped at 500
rows, sharing the Phase 1 delta sequence guard so it never overtakes a
fresher broadcast). Never rebuilds rows or triggers Regroup/LoadForList, so
it stays decoupled from the parallel Phase 2b virtualization work. The same
cadence now refreshes the long-lived Worktrees Overview, Log Visualizer, and
Merge Helper selection overlays; short-lived modals are untouched.

src/ClaudeDo.Ui/ViewModels/Modals/WorktreesOverviewModalViewModel.cs

@@ -100,8 +100,20 @@ public sealed partial class WorktreesOverviewModalViewModel : ViewModelBase
         _worker = worker;
         _diffVmFactory = diffVmFactory;
         _merge = merge;
+        // Phase 3 reconcile tick: this overlay is long-lived (stays open while the user reviews
+        // worktrees), so refresh it on the same cadence as TasksIslandViewModel's tick instead of
+        // leaving it frozen at the moment it was opened. Skipped while a load or batch merge is
+        // already in flight — reloading mid-merge would replace the row instances the merge loop
+        // is still updating.
+        _reconcileTimer.Elapsed += (_, _) =>
+            Avalonia.Threading.Dispatcher.UIThread.Post(() => _ = ReconcileTickAsync());
+        _reconcileTimer.Start();
     }
 
+    private readonly System.Timers.Timer _reconcileTimer = new(4_000);
+
+    internal Task ReconcileTickAsync() => IsBusy || IsMerging ? Task.CompletedTask : LoadAsync();
+
     public void SelectRow(WorktreeOverviewRowViewModel row)
     {
         if (SelectedRow is not null) SelectedRow.IsSelected = false;
@@ -179,7 +191,12 @@ public sealed partial class WorktreesOverviewModalViewModel : ViewModelBase
     }
 
     [RelayCommand]
-    private void Close() => CloseAction?.Invoke();
+    private void Close()
+    {
+        _reconcileTimer.Stop();
+        _reconcileTimer.Dispose();
+        CloseAction?.Invoke();
+    }
 
     [RelayCommand]
     private void ShowDiff(WorktreeOverviewRowViewModel? row)