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/config.json

@@ -19,6 +19,7 @@
     "smtp_password": { "label": "SMTP password", "hint": "App password. Stored encrypted; write-only — it's never shown back." },
     "quota_daily_budget": { "label": "Daily quota budget", "hint": "Total YouTube Data API units to spend per day (free tier is 10,000). Default 9000 leaves headroom." },
     "backfill_quota_reserve": { "label": "Backfill quota reserve", "hint": "Units kept in reserve so scheduled backfill never starves interactive syncs / enrichment." },
+    "search_daily_limit_per_user": { "label": "Live search — daily limit per user", "hint": "Max live YouTube searches per user per day. Each search costs 100 units, so the shared budget only affords ~80-90/day total. Set 0 to disable live search." },
     "backfill_recent_max_videos": { "label": "Recent backfill — max videos", "hint": "Newest videos fetched per channel on the first pass." },
     "backfill_recent_max_days": { "label": "Recent backfill — max age (days)", "hint": "How far back the first pass reaches per channel." },
     "shorts_probe_max_seconds": { "label": "Shorts probe — max duration (s)", "hint": "Only videos at or below this length are probed as possible Shorts." },

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)"
+  }
 }

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

@@ -1,6 +1,8 @@
 {
   "feed": "Feed",
   "searchPlaceholder": "Search your subscriptions…",
+  "searchYoutube": "Search YouTube",
+  "searchYoutubeTip": "Search live on YouTube for this term (uses shared API quota). You can also press Enter.",
   "channelManager": "Channel manager",
   "usageStats": "Usage & stats",
   "scheduler": "Scheduler",

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

@@ -8,6 +8,7 @@
   "videos_backfill_full": "Full-history backfill",
   "videos_enrich": "Video enrichment",
   "videos_lookup": "Video lookup",
+  "videos_search": "Live search",
   "channels_discover": "Channel discovery",
   "channels_subscribe": "Subscribe",
   "channels_unsubscribe": "Unsubscribe",