### 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_
invocation_context.data = data.get("body")
            invocation_context.headers = data.get("headers", {})
        req_start_time = datetime.now()
        result = invoke_rest_api_from_request(invocation_context)
        req_end_time = datetime.now()
        
        
        log = log_template(
            request_id=invocation_context.context["requestId"],
            date=req_start_time,
            http_method=invocation_context.method,
            resource_path=invocation_context.invocation_path,
            request_path="",
            query_string="",
            request_headers="",
            request_body="",
            response_body="",
            response_headers=result.headers,
            status_code=result.status_code,
        )
        return TestInvokeMethodResponse(
            status=result.status_code,
            headers=dict(result.headers),
            body=to_str(result.content),
            log=log,
            latency=int((req_end_time - req_start_time).total_seconds()),
            multiValueHeaders=multi_value_dict_for_list(result.headers),
        )
    @handler("CreateRestApi", expand=False)
    def create_rest_api(self, context: RequestContext, request: CreateRestApiRequest) -> RestApi: