### 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`
__slots__ = ["vtl"]
    def __init__(self):
        self.vtl = ApiGatewayVtlTemplate()
    def render(self, api_context: ApiInvocationContext) -> Union[bytes, str]:
        pass
    def render_vtl(self, template, variables):
        return self.vtl.render_vtl(template, variables=variables)
    @staticmethod
    def build_variables_mapping(api_context: ApiInvocationContext):
        
        return {
            "context": api_context.context or {},
            "stage_variables": api_context.stage_variables or {},
            "input": {
                "body": api_context.data_as_string(),
                "params": {
                    "path": api_context.path_params,
                    "querystring": api_context.query_params(),
                    "header": api_context.headers,
                },
            },
        }
class RequestTemplates(Templates):