### 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`
if "requestModels" not in resource or not resource["requestModels"]:
            return False
        schema_name = resource["requestModels"].get(APPLICATION_JSON)
        model = self.apigateway_client.get_model(
            restApiId=self.context.api_id,
            modelName=schema_name,
        )
        if not model:
            return False
        try:
            validate(instance=json.loads(self.context.data), schema=json.loads(model["schema"]))
            return True
        except ValidationError as e:
            LOG.warning("failed to validate request body", e)
            return False
    
    def validate_parameters_and_headers(self, resource):
        return True
    @staticmethod
    def should_validate_body(validator):