feat: 웹사이트 표준화 검사 도구 구현

- 4개 검사 엔진: HTML/CSS, 접근성(WCAG), SEO, 성능/보안 (총 50개 항목)
- FastAPI 백엔드 (9개 API, SSE 실시간 진행, PDF/JSON 리포트)
- Next.js 15 프론트엔드 (6개 페이지, 29개 컴포넌트, 반원 게이지 차트)
- Docker Compose 배포 (Backend:8011, Frontend:3011, MongoDB:27022, Redis:6392)
- 전체 테스트 32/32 PASS

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/app/core/database.py

@@ -0,0 +1,49 @@
+"""
+MongoDB connection management using Motor async driver.
+"""
+
+import logging
+from motor.motor_asyncio import AsyncIOMotorClient, AsyncIOMotorDatabase
+from app.core.config import get_settings
+
+logger = logging.getLogger(__name__)
+
+_client: AsyncIOMotorClient | None = None
+_db: AsyncIOMotorDatabase | None = None
+
+
+async def connect_db() -> None:
+    """Establish MongoDB connection and create indexes."""
+    global _client, _db
+    settings = get_settings()
+    _client = AsyncIOMotorClient(settings.MONGODB_URL)
+    _db = _client[settings.DB_NAME]
+
+    # Create indexes
+    await _db.inspections.create_index("inspection_id", unique=True)
+    await _db.inspections.create_index([("url", 1), ("created_at", -1)])
+    await _db.inspections.create_index([("created_at", -1)])
+
+    # Verify connection
+    await _client.admin.command("ping")
+    logger.info("MongoDB connected successfully: %s", settings.DB_NAME)
+
+
+async def close_db() -> None:
+    """Close MongoDB connection."""
+    global _client, _db
+    if _client is not None:
+        _client.close()
+        _client = None
+        _db = None
+        logger.info("MongoDB connection closed")
+
+
+def get_db() -> AsyncIOMotorDatabase:
+    """
+    Get database instance.
+    Uses 'if db is None' pattern for pymongo>=4.9 compatibility.
+    """
+    if _db is None:
+        raise RuntimeError("Database is not connected. Call connect_db() first.")
+    return _db