### 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_
create_api_context = create_custom_context(
            context,
            "CreateRestApi",
            create_api_request,
        )
        response = self.create_rest_api(create_api_context, create_api_request)
        api_id = response.get("id")
        
        store = get_apigateway_store(account_id=context.account_id, region=context.region)
        store.rest_apis[api_id].models = {}
        
        put_api_request = PutRestApiRequest(
            restApiId=api_id,
            failOnWarnings=str_to_bool(fail_on_warnings) or False,
            parameters=parameters or {},
            body=io.BytesIO(body_data),
        )
        put_api_context = create_custom_context(
            context,
            "PutRestApi",
            put_api_request,
        )
        put_api_response = self.put_rest_api(put_api_context, put_api_request)
        if not put_api_response.get("tags"):
            put_api_response.pop("tags", None)
        return put_api_response
    
    def get_integration(
        self, context: RequestContext, rest_api_id: String, resource_id: String, http_method: String
    ) -> Integration: