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/main.py

@@ -39,6 +39,7 @@ from app.routes import (
     playlists,
     quota,
     scheduler as scheduler_routes,
+    search as search_routes,
     setup as setup_routes,
     sync,
     tags,
@@ -113,6 +114,7 @@ app.include_router(auth.router)
 app.include_router(sync.router)
 app.include_router(tags.router)
 app.include_router(feed.router)
+app.include_router(search_routes.router)
 app.include_router(me.router)
 app.include_router(notifications.router)
 app.include_router(messages.router)