### 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`
_await_dynamodb_table_active(dynamodb_client, table_name)
            stream_arn = dynamodb_client.update_table(
                TableName=table_name,
                StreamSpecification={"StreamEnabled": True, "StreamViewType": "NEW_IMAGE"},
            )["TableDescription"]["LatestStreamArn"]
            event_source_uuid = lambda_client.create_event_source_mapping(
                FunctionName=function_name,
                BatchSize=1,
                StartingPosition="LATEST",
                EventSourceArn=stream_arn,
                MaximumBatchingWindowInSeconds=1,
                MaximumRetryAttempts=1,
            )["UUID"]
            _await_event_source_mapping_enabled(lambda_client, event_source_uuid)
            dynamodb_client.put_item(TableName=table_name, Item=db_item)
            retry(check_logs, retries=50, sleep=2)
        finally:
            lambda_client.delete_event_source_mapping(UUID=event_source_uuid)
    def test_disabled_dynamodb_event_source_mapping(
        self,
        create_lambda_function,
        lambda_client,
        dynamodb_resource,
        dynamodb_client,
        dynamodb_create_table,
        logs_client,
        dynamodbstreams_client,
        lambda_su_role,
    ):
        def is_stream_enabled():