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/sysconfig.py

@@ -39,6 +39,7 @@ SPECS: tuple[ConfigSpec, ...] = (
     # --- Quota (shared YouTube Data API daily budget) ---
     ConfigSpec("quota_daily_budget", "int", "quota", "quota_daily_budget", min=1, max=1_000_000),
     ConfigSpec("backfill_quota_reserve", "int", "quota", "backfill_quota_reserve", min=0, max=1_000_000),
+    ConfigSpec("search_daily_limit_per_user", "int", "quota", "search_daily_limit_per_user", min=0, max=100_000),
     # --- Backfill (recent-first first pass per channel) ---
     ConfigSpec("backfill_recent_max_videos", "int", "backfill", "backfill_recent_max_videos", min=1, max=100_000),
     ConfigSpec("backfill_recent_max_days", "int", "backfill", "backfill_recent_max_days", min=1, max=36_500),