Api gateway get output results from step function?

New Synchronous Express Workflows for AWS Step Functions is the answer: https://aws.amazon.com/blogs/compute/new-synchronous-express-workflows-for-aws-step-functions/

Amazon API Gateway now supports integration with Step Functions StartSyncExecution for HTTP APIs: https://aws.amazon.com/about-aws/whats-new/2020/12/amazon-api-gateway-supports-integration-with-step-functions-startsyncexecution-http-apis/

Update: You can now use Express Step Functions for synchronous requests.

AWS Step Functions are asynchronous and do not immediately return their results. API Gateway methods are synchronous and have a maximum timeout of 29 seconds.

To get the function output from a Step Function, you have to add a second method in API Gateway which will call the Step Function with the DescribeExecution action. The API Gateway client will have to call this periodically (poll) until the returned status is no longer "RUNNING".

Here's the DescribeExecution documentation