### 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_
"AUTHORIZER",
            "MODEL",
            "RESOURCE",
            "METHOD",
            "PATH_PARAMETER",
            "QUERY_PARAMETER",
            "REQUEST_HEADER",
            "REQUEST_BODY",
            "RESPONSE",
            "RESPONSE_HEADER",
            "RESPONSE_BODY",
        ]
        if location_type not in valid_location_types:
            raise CommonServiceException(
                "ValidationException",
                f"1 validation error detected: Value '{location_type}' at "
                f"'createDocumentationPartInput.location.type' failed to satisfy constraint: "
                f"Member must satisfy enum value set: "
                f"[RESPONSE_BODY, RESPONSE, METHOD, MODEL, AUTHORIZER, RESPONSE_HEADER, "
                f"RESOURCE, PATH_PARAMETER, REQUEST_BODY, QUERY_PARAMETER, API, REQUEST_HEADER]",
            )
        doc_part = DocumentationPart(
            id=entity_id,
            location=location,
            properties=properties,
        )
        rest_api_container.documentation_parts[entity_id] = doc_part
        result = to_documentation_part_response_json(rest_api_id, doc_part)
        return DocumentationPart(**result)
    def update_documentation_part(