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/test/postgres.test.ts

@@ -0,0 +1,29 @@
+import { describe, expect, it } from 'vitest';
+
+import { DEFAULT_POSTGRES_POOL_MAX, resolvePostgresConfigFromEnv, resolvePostgresPoolMax } from '../src/postgres.js';
+
+describe('PostgreSQL pool configuration', () => {
+    it('uses the driver-compatible default when no explicit budget exists', () => {
+        expect(resolvePostgresPoolMax(undefined)).toBe(DEFAULT_POSTGRES_POOL_MAX);
+        expect(
+            resolvePostgresConfigFromEnv({
+                env: { DATABASE_URL: 'postgresql://integration.invalid/sammo?schema=che' },
+            })
+        ).toMatchObject({ maxConnections: DEFAULT_POSTGRES_POOL_MAX });
+    });
+
+    it('accepts an explicit environment budget', () => {
+        expect(
+            resolvePostgresConfigFromEnv({
+                env: {
+                    DATABASE_URL: 'postgresql://integration.invalid/sammo?schema=che',
+                    POSTGRES_POOL_MAX: '4',
+                },
+            })
+        ).toMatchObject({ maxConnections: 4 });
+    });
+
+    it.each(['0', '-1', '1.5', '1001', 'not-a-number'])('rejects invalid pool budget %s', (value) => {
+        expect(() => resolvePostgresPoolMax(value)).toThrow(/pool max/u);
+    });
+});