feat(mission-control): give the list handler its own review task

"Let Claude handle it" now creates one ClaudeDo task per run to host the
ConPTY session (Idle/IsManual, never queued) instead of an untracked
ad-hoc tile, so the run has a real title, diff, and review outcome.
Since the handler merges its own changes straight into the list's
working dir, the task never gets a WorktreeEntity; its review range
lives as new HandlerBaseCommit/HandlerHeadCommit columns on TaskEntity
instead, reusing the existing commit-range diff machinery and keeping
it out of the worktrees overview entirely.

src/ClaudeDo.Ui/ViewModels/MissionControlViewModel.cs

@@ -294,22 +294,44 @@ public sealed partial class MissionControlViewModel : ViewModelBase, IDisposable
         return System.Threading.Tasks.Task.CompletedTask;
     }
 
-    // List-handler session over a hand-picked set of tasks ("Let Claude handle it").
-    // Ad-hoc style: no owning task, never deduped — every run opens a fresh pane.
+    // List-handler session over a hand-picked set of tasks ("Let Claude handle it"). Task-based:
+    // creates one new ClaudeDo task per run to own the session (title/diff/result), deduped by
+    // TaskId like OpenConPtySessionAsync. The handler still merges the tasks it handles itself
+    // (no worktree of its own) — see TaskEntity.HandlerBaseCommit/HandlerHeadCommit.
     public async System.Threading.Tasks.Task OpenMergeHelperConPtySessionAsync(string listId, IReadOnlyList<string> taskIds)
     {
         if (taskIds is not { Count: > 0 }) return;
 
         var title = Loc.T("missionControl.mergeHelperTitle");
+        var listName = listId;
         try
         {
             await using var ctx = await _dbFactory.CreateDbContextAsync();
             var list = await ctx.Lists.AsNoTracking().FirstOrDefaultAsync(l => l.Id == listId);
-            if (list?.Name is { Length: > 0 } name) title = $"{title} — {name}";
+            if (list?.Name is { Length: > 0 } name) { listName = name; title = $"{title} — {name}"; }
         }
         catch { /* best-effort title lookup */ }
 
-        AddConPtyPane(ConPtyPaneViewModel.CreateAdHoc(title,
+        string taskId;
+        try
+        {
+            taskId = await _worker.CreateMergeHelperTaskAsync(taskIds, listId,
+                Loc.T("missionControl.mergeHelperTaskTitle", listName),
+                Loc.T("missionControl.mergeHelperTaskDescriptionHeader"));
+        }
+        catch (Exception ex)
+        {
+            ErrorReported?.Invoke(Loc.T("missionControl.conptyLaunchFailed", ex.Message));
+            return;
+        }
+
+        if (ConPtySessions.FirstOrDefault(s => s.TaskId == taskId) is { } existing)
+        {
+            FocusedPane = existing;
+            return;
+        }
+
+        AddConPtyPane(new ConPtyPaneViewModel(taskId, title,
             () => DescribeAsync(() => _worker.GetMergeHelperLaunchSpecAsync(taskIds, listId))));
     }