### 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_
result = to_response_json("clientcertificate", data, id_attr="clientCertificateId")
    result = select_from_typed_dict(ClientCertificate, result)
    return result
def to_rest_api_response_json(data):
    result = to_response_json("restapi", data)
    result = select_from_typed_dict(RestApi, result)
    return result
def to_response_json(model_type, data, api_id=None, self_link=None, id_attr=None):
    if isinstance(data, list) and len(data) == 1:
        data = data[0]
    id_attr = id_attr or "id"
    result = deepcopy(data)
    if not self_link:
        self_link = "/%ss/%s" % (model_type, data[id_attr])
        if api_id:
            self_link = "/restapis/%s/%s" % (api_id, self_link)
    
    
    
    if "_links" not in result:
        result["_links"] = {}
    result["_links"]["self"] = {"href": self_link}
    result["_links"]["curies"] = {
        "href": "https://docs.aws.amazon.com/apigateway/latest/developerguide/restapi-authorizer-latest.html",
        "name": model_type,
        "templated": True,
    }
    result["_links"]["%s:delete" % model_type] = {"href": self_link}