fix(ui): refresh the run session id live, close the stale handoff pane

A task selected before its run started kept LatestRunSessionId null, so the
roadblock reply box and Continue stayed dead until it was re-selected.

The handoff left the Phase 1-2 tile open so its last message could be read, but
its process is gone by then and the terminal renders empty -- a dead
placeholder. It is closed on handoff now.

Also drops the WARN flood from worktree cleanup (already-unregistered worktree
and already-deleted branch are normal outcomes, not failures) and replaces the
fixed sleep in UsageGate_TransitionLogging_FiresOncePerChange with the polling
helper that already sits three lines below it in the same file.

src/ClaudeDo.Ui/ViewModels/MissionControlViewModel.cs

@@ -248,14 +248,18 @@ public sealed partial class MissionControlViewModel : ViewModelBase, IDisposable
     }
 
     // List-handler handoff: the running session called handoff_list_handler at the end of Phase 2.
-    // Opens a SECOND ConPTY tile for the SAME handler task id to carry out Phases 3-5 — deliberately
-    // NOT deduped by TaskId like OpenMergeHelperConPtySessionAsync above, since the original tile is
-    // meant to stay open (Mika closes it by hand once he has seen its last message). No new task is
-    // created here; see InteractiveLaunchSpecService.BuildForMergeHelperHandoffAsync.
+    // Replaces the Phase 1-2 tile with a fresh one for the SAME handler task id, which carries out
+    // Phases 3-5. The old tile used to be left open so its last message could still be read, but
+    // its process is gone by then and the terminal renders empty — it was only ever a dead
+    // placeholder to close by hand. No new task is created here; see
+    // InteractiveLaunchSpecService.BuildForMergeHelperHandoffAsync.
     public async System.Threading.Tasks.Task OpenMergeHelperHandoffConPtySessionAsync(string taskId, IReadOnlyList<string> survivingTaskIds)
     {
         if (string.IsNullOrEmpty(taskId) || survivingTaskIds is not { Count: > 0 }) return;
 
+        foreach (var stale in ConPtySessions.Where(s => s.TaskId == taskId).ToList())
+            CloseConPtySession(stale);
+
         var baseTitle = Loc.T("missionControl.mergeHelperTitle");
         var title = baseTitle + Loc.T("missionControl.mergeHelperHandoffTitleSuffix");
         try