### 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_
api_name = f"rest-api-{short_uid()}"
    deploy_cfn_template(
        template=TEST_TEMPLATE_1,
        parameters={"ApiName": api_name, "IntegrationUri": echo_http_server_post},
    )
    
    apis = [
        api for api in aws_client.apigateway.get_rest_apis()["items"] if api["name"] == api_name
    ]
    assert len(apis) == 1
    api_id = apis[0]["id"]
    
    url = api_invoke_url(api_id, stage="dev", path="/test")
    
    result = requests.post(url, data="test 123")
    assert result.ok
    content = json.loads(to_str(result.content))
    assert content["data"] == "test 123"
    assert content["url"].endswith("/post")
@pytest.mark.only_localstack
def test_url_output(tmp_http_server, deploy_cfn_template):