### 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_
return "AWS::ApiGateway::DomainName"
    def fetch_state(self, stack_name, resources):
        return connect_to().apigateway.get_domain_name(domainName=self.props["DomainName"])
    @staticmethod
    def get_deploy_templates():
        def _handle_result(result, resource_id, resources, resource_type):
            resources[resource_id]["PhysicalResourceId"] = result["domainName"]
        return {
            "create": {
                "function": "create_domain_name",
                "parameters": {
                    "certificateArn": lambda_keys_to_lower("CertificateArn"),
                    "domainName": lambda_keys_to_lower("DomainName"),
                    "endpointConfiguration": lambda_keys_to_lower("EndpointConfiguration"),
                    "mutualTlsAuthentication": lambda_keys_to_lower("MutualTlsAuthentication"),
                    "ownershipVerificationCertificateArn": lambda_keys_to_lower(
                        "OwnershipVerificationCertificateArn"
                    ),
                    "regionalCertificateArn": lambda_keys_to_lower("RegionalCertificateArn"),
                    "securityPolicy": lambda_keys_to_lower("SecurityPolicy"),
                    "tags": params_list_to_dict("Tags"),
                },
                "result_handler": _handle_result,
            }
        }
class GatewayBasePathMapping(GenericBaseModel):