### 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_
Type: AWS::ApiGateway::RestApi
        Properties:
          Name: !Ref RestApiName
          Policy:
            Version: "2012-10-17"
            Statement:
            - Sid: AllowInvokeAPI
              Action: "*"
              Effect: Allow
              Principal:
                AWS: "*"
              Resource: "*"
    Outputs:
      MyApiId:
        Value: !Ref MyApi
    """
    rest_api_name = f"api-{short_uid()}"
    stack = deploy_cfn_template(
        template=template,
        parameters={"RestApiName": rest_api_name},
    )
    snapshot.add_transformer(snapshot.transform.cloudformation_api())
    snapshot.add_transformer(snapshot.transform.apigateway_api())
    snapshot.add_transformer(snapshot.transform.regex(stack.stack_name, "stack-name"))
    rest_api = aws_client.apigateway.get_rest_api(restApiId=stack.outputs.get("MyApiId"))
    
    policy = to_bytes(rest_api["policy"]).decode("unicode_escape")
    rest_api["policy"] = json.loads(policy)
    snapshot.match("rest-api", rest_api)