### 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_
return item["id"]
        def filter_function(item):
            return item["name"].startswith(name_query)
        paginated_list, next_token = item_list.get_page(
            token_generator=token_generator,
            next_token=position,
            page_size=limit,
            filter_function=filter_function if name_query else None,
        )
        return ApiKeys(
            items=paginated_list, warnings=moto_response.get("warnings"), position=next_token
        )
    def update_api_key(
        self,
        context: RequestContext,
        api_key: String,
        patch_operations: ListOfPatchOperation = None,
    ) -> ApiKey:
        response: ApiKey = call_moto(context)
        if "value" in response:
            response.pop("value", None)
        if "tags" not in response:
            response["tags"] = {}
        return response
    def create_model(