### 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_id = apis[0]["id"]
    
    resources = aws_client.apigateway.get_resources(restApiId=api_id)["items"]
    assert (
        resources[0]["resourceMethods"]["GET"]["requestParameters"]["method.request.path.id"]
        is False
    )
    assert (
        resources[0]["resourceMethods"]["GET"]["methodIntegration"]["requestParameters"][
            "integration.request.path.object"
        ]
        == "method.request.path.id"
    )
    
    domain_names = [
        domain["domainName"] for domain in aws_client.apigateway.get_domain_names()["items"]
    ]
    expected_domain = "cfn5632.localstack.cloud"  
    assert expected_domain in domain_names
    
    mappings = [
        mapping["basePath"]
        for mapping in aws_client.apigateway.get_base_path_mappings(domainName=expected_domain)[
            "items"
        ]
    ]
    assert len(mappings) == 1
    assert mappings[0] == "(none)"
@pytest.mark.aws_validated
def test_cfn_apigateway_swagger_import(deploy_cfn_template, echo_http_server_post, aws_client):