Fix OBS display and Start button not working

Three issues fixed:

1. Port mismatch: The sidecar reported the OBS port (8080) in the
   ready event but the frontend needs the API port (8081). Now reports
   the API port so WebSocket/REST connects to the right place.

2. Broadcast from wrong thread: Engine init fires state_changed from
   a background thread, but _broadcast_control used get_event_loop()
   which returns the wrong loop. Now captures the uvicorn event loop
   at startup via on_event("startup").

3. Missed ready state: If the engine finishes before the WebSocket
   client connects, the "ready" state_changed was never received.
   Added status polling (GET /api/status) on WebSocket connect that
   retries every 2s while appState is "initializing".

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/api_server.py

@@ -99,11 +99,19 @@ class APIServer:
 
         self.controller.on_credits_low = on_credits_low
 
+    def set_event_loop(self, loop: asyncio.AbstractEventLoop):
+        """Set the event loop used for broadcasting (call from uvicorn startup)."""
+        self._event_loop = loop
+
     def _broadcast_control(self, data: dict):
         """Send a message to all connected /ws/control clients."""
         if not self.control_connections:
             return
 
+        loop = getattr(self, '_event_loop', None)
+        if loop is None:
+            return
+
         message = json.dumps(data)
         disconnected = []
 
@@ -111,7 +119,7 @@ class APIServer:
             try:
                 asyncio.run_coroutine_threadsafe(
                     ws.send_text(message),
-                    asyncio.get_event_loop(),
+                    loop,
                 )
             except Exception:
                 disconnected.append(ws)
@@ -124,6 +132,10 @@ class APIServer:
         app = self.app
         ctrl = self.controller
 
+        @app.on_event("startup")
+        async def on_startup():
+            self.set_event_loop(asyncio.get_event_loop())
+
         # ── Status ─────────────────────────────────────────────
 
         @app.get("/api/status")