### 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 "AWS::ApiGateway::Resource"
    def fetch_state(self, stack_name, resources):
        props = self.props
        api_id = props.get("RestApiId") or self.logical_resource_id
        parent_id = props.get("ParentId")
        if not api_id or not parent_id:
            return None
        api_resources = connect_to().apigateway.get_resources(restApiId=api_id)["items"]
        target_resource = list(
            filter(
                lambda res: res.get("parentId") == parent_id
                and res["pathPart"] == props["PathPart"],
                api_resources,
            )
        )
        if not target_resource:
            return None
        path = queries.get_apigateway_path_for_resource(
            api_id, target_resource[0]["id"], resources=api_resources
        )
        result = list(filter(lambda res: res["path"] == path, api_resources))
        return result[0] if result else None
    @staticmethod
    def get_deploy_templates():