### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

APiGateway Model that being created by CDK project stores the JSON schema with a single quotes instead of double quotes which leading to an error in parsing this json object. 

you can refere to this article to see the steps 

https://dev.to/dvddpl/reduce-lambda-invocations-and-code-boilerplate-by-adding-a-json-schema-validator-to-your-api-gateway-15af

and it works fine on AWS account 

also you can look on the attached image how localstack stores the JSON object with a single quotes, I tried to edit it manually through UI but it return it back with single quotes

![Screen Shot 2022-10-18 at 4 28 08 PM](https://user-images.githubusercontent.com/106184681/196769273-0834865a-2fb3-4efc-b3a9-9da6b2ad511d.png)

### Expected Behavior

store the json schema in correct JSON format

### How are you starting LocalStack?

With the `localstack` script

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

    localstack start

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

    cdklocal deploy


### Environment

```markdown
- OS:OSX
- LocalStack: 1.0.4
```


### Anything else?

_No response_
self, context: RequestContext, rest_api_id: String, resource_id: String, http_method: String
    ) -> None:
        try:
            call_moto(context)
        except Exception as e:
            raise NotFoundException("Invalid Resource identifier specified") from e
    
    def get_integration_response(
        self,
        context: RequestContext,
        rest_api_id: String,
        resource_id: String,
        http_method: String,
        status_code: StatusCode,
    ) -> IntegrationResponse:
        response: IntegrationResponse = call_moto(context)
        remove_empty_attributes_from_integration_response(response)
        
        
        if "selectionPattern" not in response:
            moto_rest_api = get_moto_rest_api(context, rest_api_id)
            moto_resource = moto_rest_api.resources.get(resource_id)
            method_integration = moto_resource.resource_methods[http_method].method_integration
            integration_response = method_integration.integration_responses[status_code]
            if integration_response.selection_pattern is not None:
                response["selectionPattern"] = integration_response.selection_pattern
        return response
    @handler("PutIntegrationResponse", expand=False)
    def put_integration_response(