### 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_
props = new_resource["Properties"]
        parameters_to_select = [
            "UsagePlanName",
            "Description",
            "ApiStages",
            "Quota",
            "Throttle",
            "Tags",
        ]
        update_config_props = select_attributes(props, parameters_to_select)
        if "Tags" in update_config_props:
            tags_dict = {}
            for tag in update_config_props:
                tags_dict.update({tag["Key"]: tag["Value"]})
            update_config_props["Tags"] = tags_dict
        usage_plan_id = new_resource["PhysicalResourceId"]
        patch_operations = []
        for parameter in update_config_props:
            value = update_config_props[parameter]
            if parameter == "ApiStages":
                patch_operations.append(
                    {
                        "op": "remove",
                        "path": f"/{first_char_to_lower(parameter)}",
                    }
                )