feat: 메인 화면에 정식 기수 표시

packages/infra/prisma/migrations/20260820002000_persist_official_game_index/migration.sql

@@ -0,0 +1,18 @@
+-- Ref stores server_cnt once at reset time because it is rendered on every main-page load.
+-- Backfill the active world's equivalent read-model value while excluding cancelled and
+-- unfinished history rows from the official sequence.
+UPDATE "world_state" AS ws
+SET "meta" = jsonb_set(
+    COALESCE(ws."meta", '{}'::jsonb),
+    '{gameIdx}',
+    to_jsonb((
+        SELECT COUNT(*)::integer + 1
+        FROM "ng_games" AS history
+        WHERE history."status" = 'COMPLETED'
+          AND (
+              ws."meta"->>'serverId' IS NULL
+              OR history."server_id" <> ws."meta"->>'serverId'
+          )
+    )),
+    true
+);