feat(ui): replay persisted task log when selecting a task

Read the task's LogPath on selection and feed each line through the
live-stream parser so Claude output stays visible across app restarts.
Tail-caps at 2000 lines to avoid flooding the UI.

src/ClaudeDo.Ui/ViewModels/Islands/DetailsIslandViewModel.cs

@@ -378,6 +378,9 @@ public sealed partial class DetailsIslandViewModel : ViewModelBase
             // Subscribe only after DB load confirms the task exists
             _subscribedTaskId = row.Id;
 
+            // Replay the latest run's persisted log so output is visible across app restarts.
+            await ReplayLogFileAsync(entity.LogPath, ct);
+
             var subs = await subtaskRepo.GetByTaskIdAsync(row.Id);
             ct.ThrowIfCancellationRequested();
             foreach (var s in subs)
@@ -386,6 +389,59 @@ public sealed partial class DetailsIslandViewModel : ViewModelBase
         catch (OperationCanceledException) { }
     }
 
+    private async System.Threading.Tasks.Task ReplayLogFileAsync(string? logPath, CancellationToken ct)
+    {
+        if (string.IsNullOrWhiteSpace(logPath)) return;
+        var expanded = ExpandUserPath(logPath);
+        if (!System.IO.File.Exists(expanded)) return;
+
+        try
+        {
+            const int maxLines = 2000;
+            string[] all;
+            await using (var fs = new System.IO.FileStream(
+                             expanded,
+                             System.IO.FileMode.Open,
+                             System.IO.FileAccess.Read,
+                             System.IO.FileShare.ReadWrite | System.IO.FileShare.Delete))
+            using (var reader = new System.IO.StreamReader(fs))
+            {
+                var list = new List<string>();
+                while (await reader.ReadLineAsync(ct) is { } line)
+                    list.Add(line);
+                all = list.ToArray();
+            }
+            ct.ThrowIfCancellationRequested();
+
+            var start = Math.Max(0, all.Length - maxLines);
+            for (int i = start; i < all.Length; i++)
+            {
+                ct.ThrowIfCancellationRequested();
+                if (_subscribedTaskId is null) return;
+                // Worker writes raw Claude CLI stdout to disk (no prefix) but broadcasts
+                // it with a "[stdout] " prefix. Match the live-stream format so the same
+                // stream-json parser handles both.
+                var line = all[i];
+                var normalized = line.StartsWith("[", StringComparison.Ordinal) ? line : "[stdout] " + line;
+                OnTaskMessage(_subscribedTaskId, normalized);
+            }
+            FlushClaudeBuffer();
+        }
+        catch (OperationCanceledException) { throw; }
+        catch { /* best-effort replay */ }
+    }
+
+    private static string ExpandUserPath(string path)
+    {
+        if (path.StartsWith("~/", StringComparison.Ordinal) || path.StartsWith("~\\", StringComparison.Ordinal))
+            return System.IO.Path.Combine(
+                Environment.GetFolderPath(Environment.SpecialFolder.UserProfile),
+                path[2..]);
+        if (path == "~")
+            return Environment.GetFolderPath(Environment.SpecialFolder.UserProfile);
+        return path;
+    }
+
     private async System.Threading.Tasks.Task RefreshWorktreeAsync(string taskId)
     {
         try