feat(search): live YouTube search UI

Surface live YouTube search in the existing feed, triggered explicitly so the
expensive API call is never per-keystroke.

- Header: the search box still filters the local catalog as you type; Enter or a
  YouTube button escalates the term to a live search (hidden for the demo account).
- Feed: a dedicated infinite query renders results in the same VirtualFeed cards +
  in-app player, under a banner with a back button and a quota note. No auto-paginate
  (each page spends 100 units) — an explicit 'Load more (uses quota)' button instead;
  quota/limit errors (incl. 429) shown inline. The empty local feed offers a
  'Search YouTube for <q>' CTA.
- Library: a 'Search-discovered' toggle reveals search-ingested videos (hidden by
  default); sent as exclude_search_discovered.
- Admin: search_daily_limit_per_user config field; new videos_search quota label.
- All new strings translated in HU/EN/DE.

frontend/src/i18n/locales/en/feed.json

@@ -29,5 +29,17 @@
   "undo": "Undo",
   "markedWatchedNamed": "Marked watched “{{title}}”",
   "markedWatched": "Marked watched",
-  "unwatch": "Unwatch"
+  "unwatch": "Unwatch",
+  "searchDiscovered": "Search-discovered",
+  "searchDiscoveredTip": "Also show videos that entered the library only through a live YouTube search.",
+  "yt": {
+    "searchFor": "Search YouTube for “{{query}}”",
+    "resultsFor": "YouTube results for “{{query}}”",
+    "quotaNote": "Live results — uses shared API quota",
+    "back": "Back to feed",
+    "searching": "Searching YouTube…",
+    "noResults": "No YouTube videos found.",
+    "error": "YouTube search failed.",
+    "loadMore": "Load more (uses quota)"
+  }
 }