### 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_
raise Exception(
                                "The ETag provided for the S3BodyLocation does not match the S3 Object"
                            )
                    body = get_obj_req["Body"].read()
                put_kwargs = {}
                if import_mode := props.get("Mode"):
                    put_kwargs["mode"] = import_mode
                if fail_on_warnings_mode := props.get("FailOnWarnings"):
                    put_kwargs["failOnWarnings"] = fail_on_warnings_mode
                client.put_rest_api(
                    restApiId=result["id"],
                    body=to_bytes(body),
                    parameters=import_parameters,
                    **put_kwargs,
                )
            props["id"] = result["id"]
            return result
        def _handle_result(result, resource_id, resources, resource_type):
            resources[resource_id]["PhysicalResourceId"] = result["id"]
        return {
            "create": {"function": _create, "result_handler": _handle_result},
            "delete": {
                "function": "delete_rest_api",
                "parameters": {
                    "restApiId": _api_id,
                },
            },
        }
class GatewayDeployment(GenericBaseModel):