### 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_
OpenAPIExt,
    apply_json_patch_safe,
    get_apigateway_store,
    import_api_from_openapi_spec,
    is_greedy_path,
    is_variable_path,
    log_template,
    multi_value_dict_for_list,
    resolve_references,
)
from localstack.services.apigateway.invocations import invoke_rest_api_from_request
from localstack.services.apigateway.models import RestApiContainer
from localstack.services.apigateway.patches import apply_patches
from localstack.services.apigateway.router_asf import ApigatewayRouter, to_invocation_context
from localstack.services.edge import ROUTER
from localstack.services.moto import call_moto, call_moto_with_request
from localstack.services.plugins import ServiceLifecycleHook
from localstack.utils.collections import (
    DelSafeDict,
    PaginatedList,
    ensure_list,
    select_from_typed_dict,
)
from localstack.utils.json import parse_json_or_yaml
from localstack.utils.strings import short_uid, str_to_bool, to_str
from localstack.utils.time import now_utc
LOG = logging.getLogger(__name__)
class ApigatewayProvider(ApigatewayApi, ServiceLifecycleHook):
    router: ApigatewayRouter
    def __init__(self, router: ApigatewayRouter = None):