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/routers/health.py

@@ -0,0 +1,50 @@
+"""
+Health check router.
+GET /api/health
+"""
+
+import logging
+from datetime import datetime, timezone
+
+from fastapi import APIRouter
+
+from app.core.database import get_db
+from app.core.redis import get_redis
+
+logger = logging.getLogger(__name__)
+
+router = APIRouter()
+
+
+@router.get("/health")
+async def health_check():
+    """Check system health including MongoDB and Redis connectivity."""
+    services = {}
+
+    # Check MongoDB
+    try:
+        db = get_db()
+        await db.command("ping")
+        services["mongodb"] = "connected"
+    except Exception as e:
+        logger.error("MongoDB health check failed: %s", str(e))
+        services["mongodb"] = "disconnected"
+
+    # Check Redis
+    try:
+        redis = get_redis()
+        await redis.ping()
+        services["redis"] = "connected"
+    except Exception as e:
+        logger.error("Redis health check failed: %s", str(e))
+        services["redis"] = "disconnected"
+
+    # Overall status
+    all_connected = all(v == "connected" for v in services.values())
+    status = "healthy" if all_connected else "degraded"
+
+    return {
+        "status": status,
+        "timestamp": datetime.now(timezone.utc).isoformat(),
+        "services": services,
+    }