perf: 프로필 DB 풀과 advisory lock 격리

역할별 PostgreSQL pool 상한과 동일 process 공유 pool을 적용하고 health 지표를 노출한다.\n\n게임 기능 advisory lock을 schema namespace로 통일하고 실제 PostgreSQL 통합 하네스를 보강한다.

packages/infra/src/gameSchemaAdvisoryLock.ts

@@ -0,0 +1,32 @@
+import { GamePrisma, type GamePrismaClient } from './gamePrisma.js';
+
+type GameSchemaAdvisoryLockDatabase = Pick<GamePrismaClient, '$executeRaw' | '$queryRaw'>;
+
+interface TryLockRow {
+    acquired: boolean;
+}
+
+const lockKeySql = (logicalKey: string): GamePrisma.Sql =>
+    GamePrisma.sql`hashtextextended(current_schema() || chr(31) || ${logicalKey}, 0)`;
+
+/**
+ * Acquires a transaction-scoped lock whose namespace is the active game schema.
+ * Callers must already be inside the transaction that owns the protected write.
+ */
+export const acquireGameSchemaAdvisoryXactLock = async (
+    database: GameSchemaAdvisoryLockDatabase,
+    logicalKey: string
+): Promise<void> => {
+    await database.$executeRaw(GamePrisma.sql`SELECT pg_advisory_xact_lock(${lockKeySql(logicalKey)})`);
+};
+
+/** Test and diagnostics boundary matching acquireGameSchemaAdvisoryXactLock. */
+export const tryGameSchemaAdvisoryXactLock = async (
+    database: GameSchemaAdvisoryLockDatabase,
+    logicalKey: string
+): Promise<boolean> => {
+    const rows = await database.$queryRaw<TryLockRow[]>(
+        GamePrisma.sql`SELECT pg_try_advisory_xact_lock(${lockKeySql(logicalKey)}) AS acquired`
+    );
+    return rows[0]?.acquired === true;
+};