feat(J): WebSocket live-events + replace polling + fix ffmpeg turntable timeout

- fix(render): ffmpeg overlay=0:0 -> overlay=0:0:shortest=1 to prevent hang on finite PNG sequences
- feat(ws): add core/websocket.py ConnectionManager + Redis Pub/Sub subscriber loop
- feat(ws): add /api/ws WebSocket endpoint with JWT query-param auth in main.py
- feat(ws): emit render_complete/failed + cad_processing_complete events from step_tasks.py
- feat(ws): emit order_status_change events from orders router
- feat(ws): add beat_tasks.py broadcast_queue_status task (every 10s via Redis __broadcast__)
- feat(frontend): add useWebSocket hook with auto-reconnect (exponential backoff, 25s ping)
- feat(frontend): add WebSocketContext + WebSocketProvider wrapping App
- refactor(frontend): remove polling from WorkerActivity (was 5s/3s) + OrderDetail (was 5s)
- refactor(frontend): reduce polling in Layout (8s->60s) + NotificationCenter (15s->60s)
- docs: add ffmpeg shortest=1 + WebSocket JWT auth learnings to LEARNINGS.md

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/tasks/beat_tasks.py

@@ -0,0 +1,33 @@
+"""Celery Beat periodic tasks."""
+from __future__ import annotations
+
+import json
+import logging
+
+from celery import shared_task
+
+logger = logging.getLogger(__name__)
+
+
+@shared_task(name="app.tasks.beat_tasks.broadcast_queue_status", queue="step_processing")
+def broadcast_queue_status() -> None:
+    """Broadcast current queue depths to all WebSocket clients every 10s.
+
+    Publishes to the Redis '__broadcast__' channel which the WebSocket
+    subscriber in the FastAPI process forwards to all connected clients.
+    """
+    try:
+        import redis as sync_redis
+        from app.config import settings
+
+        r = sync_redis.from_url(settings.redis_url, decode_responses=True)
+        depths = {
+            "step_processing": r.llen("step_processing"),
+            "thumbnail_rendering": r.llen("thumbnail_rendering"),
+        }
+        event = {"type": "queue_update", "depths": depths}
+        r.publish("__broadcast__", json.dumps(event))
+        r.close()
+        logger.debug("Broadcast queue_update: %s", depths)
+    except Exception as exc:
+        logger.warning("broadcast_queue_status failed: %s", exc)