(feat) log error class, function_name on prometheus service failure hook + only log DB related failures on DB service hook (#6650)

* log error on prometheus service failure hook

* use a more accurate function name for wrapper that handles logging db metrics

* fix log_db_metrics

* test_log_db_metrics_failure_error_types

* fix linting

* fix auth checks

litellm/_service_logger.py

@@ -241,7 +241,8 @@ class ServiceLogging(CustomLogger):
             if callback == "prometheus_system":
                 await self.init_prometheus_services_logger_if_none()
                 await self.prometheusServicesLogger.async_service_failure_hook(
-                    payload=payload
+                    payload=payload,
+                    error=error,
                 )
             elif callback == "datadog":
                 await self.init_datadog_logger_if_none()