### 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::UsagePlanKey"
    def fetch_state(self, stack_name, resources):
        client = connect_to().apigateway
        key_id = self.props.get("KeyId")
        key_type = self.props.get("KeyType")
        plan_id = self.props.get("UsagePlanId")
        result = client.get_usage_plan_keys(usagePlanId=plan_id).get("items", [])
        result = [r for r in result if r["id"] == key_id and key_type in [None, r.get("type")]]
        return (result or [None])[0]
    @staticmethod
    def get_deploy_templates():
        def _handle_result(result, resource_id, resources, resource_type):
            resources[resource_id]["PhysicalResourceId"] = result["id"]
        return {
            "create": {
                "function": "create_usage_plan_key",
                "parameters": lambda_keys_to_lower(),
                "result_handler": _handle_result,
            }
        }
class GatewayDomain(GenericBaseModel):
    @staticmethod
    def cloudformation_type():