Filter health check logs from uvicorn access log

Add HealthCheckFilter to suppress /health endpoint logs at INFO level,
reducing noise from Docker healthcheck requests every 30 seconds.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/main.py

@@ -18,6 +18,19 @@ logging.basicConfig(
     datefmt="%Y-%m-%d %H:%M:%S"
 )
 logger = logging.getLogger(__name__)
+
+
+class HealthCheckFilter(logging.Filter):
+    """Filter out health check endpoint logs from uvicorn access log."""
+    def filter(self, record: logging.LogRecord) -> bool:
+        message = record.getMessage()
+        if "GET /health" in message:
+            return False
+        return True
+
+
+# Filter out health check logs from uvicorn access log
+logging.getLogger("uvicorn.access").addFilter(HealthCheckFilter())
 from app.websocket.manager import ConnectionManager
 from app.websocket.handlers import handle_analyze_message
 from app.services.gemini_service import GeminiService