Вы должны использовать aws_api_gateway_method_settings
...
resource "aws_api_gateway_method_settings" "YOUR_settings" {
rest_api_id = "${aws_api_gateway_rest_api.YOUR.id}"
stage_name = "${aws_api_gateway_stage.YOUR.stage_name}"
method_path = "*/*"
settings {
logging_level = "INFO"
data_trace_enabled = true
metrics_enabled = true
}
}
CloudWatch LogGroup должна выглядеть так
API-Gateway-Execution-Logs_{YOU_API_ID}/{YOU_STAGENAME}
... может быть, вам нужно настроить все роли IAM ...