feat(search): live YouTube search backend

Add a live YouTube search that materialises results into the shared catalog so
they render with the normal feed cards + in-app player and gain per-user state.

- YouTubeClient.search_videos(): search.list (100 units), embeddable-only, returns
  flat stubs + nextPageToken; surfaces liveBroadcastContent for live filtering.
- routes/search.py GET /api/search/youtube: require_human + per-user daily cap
  (search_daily_limit_per_user, default 70) + can_spend pre-check (429 on either);
  drops live/upcoming, upserts channel stubs (channels.list) + video stubs, enriches
  (videos.list), runs the youtube.com/shorts probe, then excludes Shorts/live and
  returns feed cards in relevance order with the YouTube pageToken as the cursor.
- Provenance: videos.via_search / channels.from_search (migration 0028) flag
  search-discovered rows; the feed hides them from the Library (scope=all) by default
  via exclude_search_discovered, leaving the Mine feed untouched.
- quota.actions_today() counts a user's per-action events today for the cap; only the
  search.list call is attributed VIDEOS_SEARCH so the counter is exactly 1 per search.

backend/app/config.py

@@ -71,6 +71,9 @@ class Settings(BaseSettings):
     youtube_api_proxy: str = ""
     # Daily quota budget (units). Default leaves headroom under the 10,000/day free limit.
     quota_daily_budget: int = 9000
+    # Per-user cap on live YouTube searches per day. search.list costs 100 units each, so the
+    # shared budget only affords ~80-90/day total — this stops one user draining it. Admin-tunable.
+    search_daily_limit_per_user: int = 70
     # Recent-first backfill: how far back to fetch on the first pass per channel.
     backfill_recent_max_videos: int = 100
     backfill_recent_max_days: int = 365