### 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_
test_port, invocations, proxy = tmp_http_server
    integration_uri = f"http://localhost:{test_port}/{{proxy}}"
    api_name = f"rest-api-{short_uid()}"
    stack = deploy_cfn_template(
        template_path=os.path.join(
            os.path.dirname(__file__), "../../templates/apigateway-url-output.yaml"
        ),
        template_mapping={
            "api_name": api_name,
            "integration_uri": integration_uri,
        },
    )
    assert len(stack.outputs) == 2
    api_id = stack.outputs["ApiV1IdOutput"]
    api_url = stack.outputs["ApiV1UrlOutput"]
    assert api_id
    assert api_url
    assert api_id in api_url
    assert f"https://{api_id}.execute-api.{constants.LOCALHOST_HOSTNAME}:4566" in api_url
def test_cfn_with_apigateway_resources(deploy_cfn_template, aws_client):
    stack = deploy_cfn_template(
        template_path=os.path.join(os.path.dirname(__file__), "../../templates/template35.yaml")
    )
    apis = [
        api