### 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_
for api in aws_client.apigateway.get_rest_apis()["items"]
        if api["name"] == "celeste-Gateway-local"
    ]
    assert len(apis) == 1
    api_id = apis[0]["id"]
    resources = [
        res
        for res in aws_client.apigateway.get_resources(restApiId=api_id)["items"]
        if res.get("pathPart") == "account"
    ]
    assert len(resources) == 1
    
    assert resources[0]["resourceMethods"]["POST"]["requestParameters"] == {
        "method.request.path.account": True
    }
    models = [
        model
        for model in aws_client.apigateway.get_models(restApiId=api_id)["items"]
        if stack.stack_name in model["name"]
    ]
    assert len(models) == 2
    stack.destroy()
    apis = [
        api
        for api in aws_client.apigateway.get_rest_apis()["items"]
        if api["name"] == "celeste-Gateway-local"
    ]
    assert not apis
@pytest.mark.aws_validated
def test_cfn_deploy_apigateway_integration(deploy_cfn_template, snapshot, aws_client):