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/lib/api.ts

@@ -141,6 +141,9 @@ export interface FeedFilters {
   includeShorts: boolean;
   includeLive: boolean;
   show: string;
+  // Library (scope "all") only: when set, also show videos that entered the catalog via a
+  // live YouTube search. Default (falsy) hides that search-discovered "noise".
+  showSearchDiscovered?: boolean;
   channelId?: string;
   channelName?: string;
   maxAgeDays?: number;
@@ -306,6 +309,8 @@ function filterParams(f: FeedFilters): URLSearchParams {
   if (f.dateTo) p.set("published_before", f.dateTo);
   if (f.minDuration != null) p.set("min_duration", String(f.minDuration));
   if (f.maxDuration != null) p.set("max_duration", String(f.maxDuration));
+  // Only relevant in Library scope; the backend ignores it for "my". Default = hide.
+  p.set("exclude_search_discovered", String(!f.showSearchDiscovered));
   return p;
 }
 
@@ -558,6 +563,14 @@ export const api = {
     req(`/api/feed?${feedQuery(f, cursor, limit)}`),
   feedCount: (f: FeedFilters): Promise<{ count: number }> =>
     req(`/api/feed/count?${filterParams(f).toString()}`),
+  // Live YouTube search: results are materialised into the catalog and returned as feed cards.
+  // `quiet` so the YT-search panel can render quota/limit errors (incl. 429) inline instead of
+  // popping the global modal. `cursor` is the YouTube nextPageToken (each page spends 100 units).
+  searchYoutube: (q: string, cursor: string | null): Promise<FeedResponse> => {
+    const p = new URLSearchParams({ q });
+    if (cursor) p.set("cursor", cursor);
+    return req(`/api/search/youtube?${p.toString()}`, {}, { quiet: true });
+  },
   facets: (f: FeedFilters): Promise<{ counts: Record<string, number> }> =>
     req(`/api/facets?${filterParams(f).toString()}`),
   // idempotent: setting a state / saving a progress checkpoint is safe to replay, so these