### 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`
self.context = context
        self.apigateway_client = apigateway_client
    def is_request_valid(self) -> bool:
        
        if self.context.resource is None or "resourceMethods" not in self.context.resource:
            return True
        resource_methods = self.context.resource["resourceMethods"]
        if self.context.method not in resource_methods:
            return True
        
        resource = resource_methods[self.context.method]
        if not (resource.get("requestValidatorId") or "").strip():
            return True
        
        validator = self.apigateway_client.get_request_validator(
            restApiId=self.context.api_id, requestValidatorId=resource["requestValidatorId"]
        )
        if validator is None:
            return True
        
        if self.should_validate_body(validator):
            is_body_valid = self.validate_body(resource)
            if not is_body_valid:
                return is_body_valid
        if self.should_validate_request(validator):
            is_valid_parameters = self.validate_parameters_and_headers(resource)
            if not is_valid_parameters:
                return is_valid_parameters
        return True
    def validate_body(self, resource):