### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I Created an REST APIGatway with lambda handler using AWS CDK. when I hit the API the response header content type is always  set to "text/html"  instead of `application/json` . even if I changed the response template or added the header to lambda returned response. when I deploy the same stack on AWS account  the response header is fine and work as expected

### Expected Behavior

Response Header content-type to be `application/json`

### How are you starting LocalStack?

  `localstack start` command

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command`)

    `localstack start` command

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

I'm using AWS CDK typescript application and deploy it using `cdklocal` command on localstack

Using CDK follow the steps:
- create  REST ApiGateway
- create Lambda function 
- integrate lambda with APIGatway

On Command line:
- deploy using `cdklocal deploy` command

Finally
- test the endpoint and check the response header content-type




### Environment

```markdown
- OS: Windows 
- LocalStack: latest
```


### Anything else?

When I deploy the same stack on AWS account everything works fine and the response header content-type is `application/json`
except AttributeError:
                msg = "Invalid step function action: %s" % method_name
                LOG.error(msg)
                return make_error_response(msg, 400)
            result = method(**payload)
            result = json_safe({k: result[k] for k in result if k not in "ResponseMetadata"})
            response = requests_response(
                content=result,
                headers=aws_stack.mock_aws_request_headers(),
            )
            if action == "StartSyncExecution":
                
                result = await_sfn_execution_result(result["executionArn"])
                result_status = result.get("status")
                if result_status != "SUCCEEDED":
                    return make_error_response(
                        "StepFunctions execution %s failed with status '%s'"
                        % (result["executionArn"], result_status),
                        500,
                    )
                result = json_safe(result)
                response = requests_response(content=result)
            
            invocation_context.response = response
            response_templates = ResponseTemplates()
            response_templates.render(invocation_context)
            
            
            
            return response