### 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`
pass
    def __init__(self, passthrough_behaviour: str):
        self.passthrough_behavior = self.get_passthrough_behavior(passthrough_behaviour)
    def check_passthrough_behavior(self, request_template):
        """
        Specifies how the method request body of an unmapped content type will be passed through
        the integration request to the back end without transformation.
        A content type is unmapped if no mapping template is defined in the integration or the
        content type does not match any of the mapped content types, as specified in requestTemplates
        """
        if not request_template and self.passthrough_behavior in {
            PassthroughBehavior.NEVER,
            PassthroughBehavior.WHEN_NO_TEMPLATES,
        }:
            raise MappingTemplates.UnsupportedMediaType()
    @staticmethod
    def get_passthrough_behavior(passthrough_behaviour: str):
        return getattr(PassthroughBehavior, passthrough_behaviour, None)
class BackendIntegration(ABC):
    """Abstract base class representing a backend integration"""
    def __init__(self):
        self.request_templates = RequestTemplates()
        self.response_templates = ResponseTemplates()
    @abstractmethod
    def invoke(self, invocation_context: ApiInvocationContext):
        pass
    @classmethod
    def _create_response(cls, status_code, headers, data=""):