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.Worker/Worktrees/WorktreeMaintenanceService.cs

@@ -143,8 +143,15 @@ public sealed class WorktreeMaintenanceService
             }
             catch (Exception ex)
             {
-                _logger.LogWarning(ex,
-                    "git worktree remove failed for {Path}; falling back to directory delete", row.Path);
+                // "is not a working tree" means git already forgot this worktree (pruned, or
+                // removed by hand). Deleting the directory is then the whole job, not a fallback
+                // from a real failure -- warning about it floods the footer log strip when a
+                // batch of stale rows is cleaned up.
+                if (IsAlreadyUnregistered(ex))
+                    _logger.LogDebug(ex, "git no longer tracks {Path}; deleting the directory", row.Path);
+                else
+                    _logger.LogWarning(ex,
+                        "git worktree remove failed for {Path}; falling back to directory delete", row.Path);
                 try { if (Directory.Exists(row.Path)) Directory.Delete(row.Path, recursive: true); }
                 catch (Exception delEx)
                 {
@@ -186,8 +193,12 @@ public sealed class WorktreeMaintenanceService
                 }
                 catch (Exception ex)
                 {
-                    _logger.LogWarning(ex, "Failed to delete branch {Branch} for worktree {Path}",
-                        row.BranchName, row.Path);
+                    // Already deleted -- the normal case once the branch has been merged.
+                    if (IsBranchAlreadyGone(ex))
+                        _logger.LogDebug(ex, "branch {Branch} was already deleted", row.BranchName);
+                    else
+                        _logger.LogWarning(ex, "Failed to delete branch {Branch} for worktree {Path}",
+                            row.BranchName, row.Path);
                 }
             }
         }
@@ -197,5 +208,12 @@ public sealed class WorktreeMaintenanceService
         return (true, branchDeleted);
     }
 
+    // Both are "already done" outcomes, not failures — see the call sites.
+    private static bool IsAlreadyUnregistered(Exception ex) =>
+        ex.Message.Contains("is not a working tree", StringComparison.OrdinalIgnoreCase);
+
+    private static bool IsBranchAlreadyGone(Exception ex) =>
+        ex.Message.Contains("' not found", StringComparison.Ordinal);
+
     private sealed record WorktreeRow(string TaskId, string Path, string BranchName, string? WorkingDir);
 }