### 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_
self, context: RequestContext, domain_name: String, base_path: String
    ) -> None:
        region_details = get_apigateway_store()
        mappings_list = region_details.base_path_mappings.get(domain_name) or []
        for i in range(len(mappings_list)):
            if mappings_list[i]["basePath"] == base_path:
                del mappings_list[i]
                return
        raise NotFoundException(f"Base path mapping {base_path} for domain {domain_name} not found")
    
    def get_client_certificate(
        self, context: RequestContext, client_certificate_id: String
    ) -> ClientCertificate:
        region_details = get_apigateway_store()
        result = region_details.client_certificates.get(client_certificate_id)
        if result is None:
            raise NotFoundException(f"Client certificate ID {client_certificate_id} not found")
        return ClientCertificate(**result)
    def get_client_certificates(
        self, context: RequestContext, position: String = None, limit: NullableInteger = None
    ) -> ClientCertificates:
        region_details = get_apigateway_store()
        result = list(region_details.client_certificates.values())
        return ClientCertificates(items=result)
    def generate_client_certificate(