perf(labrinth/random_projects_get): speed up through spatial queries according to profiling results (#3762)

apps/labrinth/migrations/20250609134334_spatial-random-project-index.sql

@@ -0,0 +1,12 @@
+-- The spatial query for retrieving random searchable projects is greatly sped
+-- up by this index on a fixture of 1M mods, bringing down the total cost of
+-- the query plan and runtime to be comparable to primary key lookups. See the
+-- `labrinth::routes::v3::projects::random_projects_get` function and the
+-- previous 20250608183828_random-project-index.sql migration for more details.
+--
+-- That previous migration created a non-spatial index for the status column which
+-- does not get used in the new spatial query, but may still be useful for other
+-- queries that filter mods by status.
+
+CREATE INDEX mods_searchable_ids_gist ON mods USING gist (POINT(id, 0))
+    WHERE status = ANY(ARRAY['approved', 'archived']);