Persistent server search cache: 200 results per query, 250k queries, 15-day stale-while-revalidate, refresh=1

server/db.js

@@ -112,6 +112,17 @@ export async function initDb() {
     CREATE INDEX IF NOT EXISTS idx_media_lru
       ON media_cache (status, last_access);
 
+    -- Persistent search cache: the YouTube part of a search (up to 200 cards,
+    -- JSON), keyed by the lowercased query. Trimmed LRU by count and bytes.
+    CREATE TABLE IF NOT EXISTS search_cache (
+      q           TEXT    PRIMARY KEY,
+      results     TEXT    NOT NULL,
+      size        INTEGER NOT NULL DEFAULT 0,
+      fetched_at  INTEGER NOT NULL DEFAULT 0,
+      last_access INTEGER NOT NULL DEFAULT 0
+    );
+    CREATE INDEX IF NOT EXISTS idx_search_cache_lru ON search_cache (last_access);
+
     -- Shared per-video documents (kind = lyrics | chapters), visible to every
     -- user. The live copy is here; every save also lands in video_note_revs
     -- as a full snapshot, which is the server-side backup and undo history.