feat: centralized PTY-scoped session state, sync engine debug panel, lifecycle states, WS monitor

- Refactor session state to use ptySessionId as primary key across all components
- Add SessionStateManager with PTY-scoped hook processing, approval tracking, notifications
- Add sync-engine debug panel (AgentStatesSection, HookTimelineSection, TerminalRegistrySection, WsMonitorSection)
- Add useLifecycleStates composable for continuous state chips (session, responding, tool, subagent, compacting)
- Add WS monitor endpoint and composable for real-time connection health
- Enhance SessionLifecycleStatus with animated state chips and badge counts
- Enhance SystemMessage with expanded content and better formatting
- Update hooks (approval-permission, approval-plan, notify) with pty_session injection
- Update approval system to derive pending lists from PTY-scoped state
- Update ChatContainer with PTY-derived agent status and lifecycle events
- Update AgentBadge with PTY-scoped status colors
- Improve PiP window, approval window, and loading window handling

frontend/public/loading.html

@@ -35,8 +35,22 @@
     <div class="badge" id="b"></div>
   </div>
   <script>
+    var badge = document.getElementById('b');
+    function updateBadge(n) {
+      if (n > 1) { badge.textContent = n; badge.className = 'badge show'; }
+      else { badge.className = 'badge'; }
+    }
+
+    // Initial count from query param
     var c = new URLSearchParams(location.search).get('n');
-    if (c && parseInt(c) > 1) { var b = document.getElementById('b'); b.textContent = c; b.className = 'badge show'; }
+    if (c) updateBadge(parseInt(c));
+
+    // Live updates via Tauri event (no module imports needed)
+    var T = window.__TAURI_INTERNALS__;
+    if (T) {
+      var handler = T.transformCallback(function(ev) { updateBadge(ev.payload); });
+      T.invoke('plugin:event|listen', { event: 'loading:count', target: { kind: 'Any' }, handler: handler });
+    }
   </script>
 </body>
 </html>