### 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`
queue_name_1 = f"queue-{short_uid()}-1"
        queue_name_2 = f"queue-{short_uid()}-2"
        queue_url_1 = sqs_create_queue(QueueName=queue_name_1)
        queue_arn_1 = sqs_queue_arn(queue_url_1)
        try:
            create_lambda_function(
                func_name=function_name,
                handler_file=TEST_LAMBDA_PYTHON_ECHO,
                runtime=LAMBDA_RUNTIME_PYTHON36,
                role=lambda_su_role,
            )
            rs = lambda_client.create_event_source_mapping(
                EventSourceArn=queue_arn_1, FunctionName=function_name
            )
            snapshot.match("create-event-source-mapping", rs)
            uuid = rs["UUID"]
            assert BATCH_SIZE_RANGES["sqs"][0] == rs["BatchSize"]
            _await_event_source_mapping_enabled(lambda_client, uuid)
            with pytest.raises(ClientError) as e:
                
                rs = lambda_client.update_event_source_mapping(
                    UUID=uuid,
                    FunctionName=function_name,
                    BatchSize=BATCH_SIZE_RANGES["sqs"][1] + 1,
                )
            snapshot.match("invalid-update-event-source-mapping", e.value.response)
            e.match(INVALID_PARAMETER_VALUE_EXCEPTION)
            queue_url_2 = sqs_create_queue(QueueName=queue_name_2)
            queue_arn_2 = sqs_queue_arn(queue_url_2)
            with pytest.raises(ClientError) as e: