### 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, description: String = None, tags: MapOfStringToString = None
    ) -> ClientCertificate:
        region_details = get_apigateway_store()
        cert_id = short_uid()
        creation_time = now_utc()
        entry = {
            "description": description,
            "tags": tags,
            "clientCertificateId": cert_id,
            "createdDate": creation_time,
            "expirationDate": creation_time + 60 * 60 * 24 * 30,  
            "pemEncodedCertificate": "testcert-123",  
        }
        region_details.client_certificates[cert_id] = entry
        result = to_client_cert_response_json(entry)
        return ClientCertificate(**result)
    def update_client_certificate(
        self,
        context: RequestContext,
        client_certificate_id: String,
        patch_operations: ListOfPatchOperation = None,
    ) -> ClientCertificate:
        region_details = get_apigateway_store()
        entity = region_details.client_certificates.get(client_certificate_id)
        if entity is None:
            raise NotFoundException(f'Client certificate ID "{client_certificate_id}" not found')
        result = apply_json_patch_safe(entity, patch_operations)
        result = to_client_cert_response_json(result)
        return ClientCertificate(**result)
    def delete_client_certificate(