feat: M2 (part 2) — RSS poller, backfill, enrichment, scheduler

- Free per-channel RSS reader for quota-less fresh-video detection
- Recent-first backfill (configurable: 100 videos / 1 year) plus resumable deep
  backfill from the uploads playlist
- Enrichment via videos.list: duration, view/like counts, category, topics,
  language, Shorts heuristic and livestream/premiere classification
- Reusable sync runners + APScheduler jobs (rss / enrich / backfill), all
  quota-aware with a reserve so backfill never starves fresh enrichment
- Manual triggers: POST /api/sync/{rss,backfill,enrich}
- Exact insert counting via RETURNING with in-batch de-duplication

backend/app/main.py

@@ -1,3 +1,4 @@
+from contextlib import asynccontextmanager
 from pathlib import Path
 
 from fastapi import FastAPI
@@ -9,8 +10,19 @@ from starlette.middleware.sessions import SessionMiddleware
 from app import auth
 from app.config import settings
 from app.routes import health, sync
+from app.scheduler import shutdown_scheduler, start_scheduler
 
-app = FastAPI(title=settings.app_name)
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    start_scheduler()
+    try:
+        yield
+    finally:
+        shutdown_scheduler()
+
+
+app = FastAPI(title=settings.app_name, lifespan=lifespan)
 
 app.add_middleware(
     SessionMiddleware,