[api] improve invention query

apps/api/migrations/0027_invention_feed_newest.sql

@@ -0,0 +1,17 @@
+-- Index the browse/search feed (`searchInventions`) in the order it pages: newest first.
+-- Without it every page — however small — parsed the JSON of every published invention,
+-- sorted the lot in a temp B-tree and threw all but one page away. With it the query walks
+-- this index in order and stops after OFFSET + LIMIT rows.
+--
+-- PARTIAL, over exactly the rows `VISIBLE_IN_FEEDS` admits, so it holds only what a feed can
+-- show. SQLite uses a partial index only when the query's WHERE contains each of these terms
+-- as written, so this WHERE must track `VISIBLE_IN_FEEDS` in src/inventions-db.ts term for
+-- term — change one and the index silently stops being used. The key is the same
+-- `json_extract` expression the query orders by, which is what lets it replace the sort.
+-- Generated from src/inventions-db.ts (SCHEMA_DDL) — keep in sync.
+
+CREATE INDEX IF NOT EXISTS idx_invention_feed_newest
+  ON invention (json_extract(data, '$.CreatedAt') DESC, id DESC)
+  WHERE is_published = 1
+    AND hide_from_player = 0
+    AND COALESCE(json_extract(data, '$.Accessibility'), 0) <> 2;