### 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_
raise BadRequestException(
                        "Model schema must have at least 1 property or array items defined"
                    )
                
                store.rest_apis[rest_api_id].resolved_models.pop(model_name, None)
            model[key] = value
        remove_empty_attributes_from_model(model)
        return model
    def delete_model(
        self, context: RequestContext, rest_api_id: String, model_name: String
    ) -> None:
        store = get_apigateway_store(account_id=context.account_id, region=context.region)
        if (
            rest_api_id not in store.rest_apis
            or model_name not in store.rest_apis[rest_api_id].models
        ):
            raise NotFoundException(f"Invalid model name specified: {model_name}")
        moto_rest_api = get_moto_rest_api(context, rest_api_id)
        validate_model_in_use(moto_rest_api, model_name)
        store.rest_apis[rest_api_id].models.pop(model_name, None)
        store.rest_apis[rest_api_id].resolved_models.pop(model_name, None)
def get_moto_rest_api(context: RequestContext, rest_api_id: str) -> MotoRestAPI:
    moto_backend = apigw_models.apigateway_backends[context.account_id][context.region]
    if rest_api := moto_backend.apis.get(rest_api_id):
        return rest_api
    else:
        raise NotFoundException(
            f"Invalid API identifier specified {context.account_id}:{rest_api_id}"
        )
def remove_empty_attributes_from_rest_api(rest_api: RestApi, remove_tags=True) -> RestApi: