Channel features: subscribers, new-videos badges, activity-driven sync

- Store subscriber count from YouTube statistics and show it on channel page
- Sync 50 videos per channel with playlistItems pagination support
- Show per-channel and per-category new-videos counters (2-day window)
- Replace hourly videos sync with activity trigger (2h idle) and
  incremental backfill (hard cap 200 per channel)
- Clicking the sidebar new-videos count filters the category feed to
  recent videos only (new_only)
- Update agent-team docs: deploy after green checks

backend/app/core/auth_dependency.py

@@ -1,6 +1,11 @@
 from fastapi import HTTPException, Request
 
+from app.services.sync_trigger import maybe_trigger_videos_sync
+
 
 def require_session(request: Request) -> None:
     if not request.session.get("authenticated"):
         raise HTTPException(status_code=401, detail="Not authenticated")
+    # Every authenticated request may trigger a background videos sync when it
+    # is due (cheap check: lock + one app_settings row read).
+    maybe_trigger_videos_sync()