feat(cli,tui): show time since last final agent response on the status bar (#44265)

Adds an idle clock to the context/status bar in both the prompt_toolkit CLI
and the Ink TUI: once a turn completes, a dim '✓ <elapsed>' segment shows how
long the session has been idle since the last final agent response. Hidden
while a turn is live (the per-prompt elapsed timer covers that) and before
the first turn completes.

- cli.py: track _last_turn_finished_at when the agent thread exits, surface
  it via _format_idle_since() in the snapshot, render in both the wide
  fragments path and the plain-text fallback.
- ui-tui: stamp lastTurnEndedAt when busy flips false after a live turn,
  thread it through appStatus -> StatusRule, render via a ticking IdleSince
  segment sharing the duration breakpoint/width budget.

cli.py

@@ -3426,6 +3426,7 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
         # frozen when the agent thread completes, displayed in the status bar.
         self._prompt_start_time: Optional[float] = None  # time.time() when turn started
         self._prompt_duration: float = 0.0  # frozen duration of last completed turn
+        self._last_turn_finished_at: Optional[float] = None  # time.time() when the last agent loop finished
         # Initialize SQLite session store early so /title works before first message
         self._session_db = None
         try:
@@ -3812,6 +3813,19 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
         emoji = "⏱" if live else "⏲"
         return f"{emoji} {time_str}"
 
+    @staticmethod
+    def _format_idle_since(last_finished_at: Optional[float], turn_live: bool) -> str:
+        """Format time since the last final agent response for the status bar.
+
+        Returns an empty string while a turn is live (the per-prompt elapsed
+        timer covers that case) or before the first turn has completed.
+        Compact read-out: ``✓ 42s`` / ``✓ 3m`` / ``✓ 1h 12m``.
+        """
+        if turn_live or last_finished_at is None:
+            return ""
+        idle = max(0.0, time.time() - last_finished_at)
+        return f"✓ {format_duration_compact(idle)}"
+
     def _get_status_bar_snapshot(self) -> Dict[str, Any]:
         # Prefer the agent's model name — it updates on fallback.
         # self.model reflects the originally configured model and never
@@ -3835,6 +3849,10 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
                 getattr(self, "_prompt_duration", 0.0),
                 live=getattr(self, "_prompt_start_time", None) is not None,
             ),
+            "idle_since": self._format_idle_since(
+                getattr(self, "_last_turn_finished_at", None),
+                turn_live=getattr(self, "_prompt_start_time", None) is not None,
+            ),
             "context_tokens": 0,
             "context_length": None,
             "context_percent": None,
@@ -4146,6 +4164,9 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
             prompt_elapsed = snapshot.get("prompt_elapsed")
             if prompt_elapsed:
                 parts.append(prompt_elapsed)
+            idle_since = snapshot.get("idle_since")
+            if idle_since:
+                parts.append(idle_since)
             if yolo_active:
                 parts.append("⚠ YOLO")
             return self._trim_status_bar_text(" │ ".join(parts), width)
@@ -4247,6 +4268,11 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
                     if prompt_elapsed:
                         frags.append(("class:status-bar-dim", " │ "))
                         frags.append(("class:status-bar-dim", prompt_elapsed))
+                    # Position 8: idle time since the last final agent response
+                    idle_since = snapshot.get("idle_since")
+                    if idle_since:
+                        frags.append(("class:status-bar-dim", " │ "))
+                        frags.append(("class:status-bar-dim", idle_since))
                     if yolo_active:
                         frags.append(("class:status-bar-dim", " │ "))
                         frags.append(("class:status-bar-yolo", "⚠ YOLO"))
@@ -10162,6 +10188,9 @@ class HermesCLI(CLIAgentSetupMixin, CLICommandsMixin):
             if self._prompt_start_time is not None:
                 self._prompt_duration = max(0.0, time.time() - self._prompt_start_time)
                 self._prompt_start_time = None
+            # Record when this agent loop finished so the status bar can show
+            # idle time since the last final response.
+            self._last_turn_finished_at = time.time()
 
             # Proactively clean up async clients whose event loop is dead.
             # The agent thread may have created AsyncOpenAI clients bound