### 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_
patch_op["path"] = f"{binary_media_types_path}/{remove_index}"
                elif patch_op["op"] == "replace":
                    
                    
                    replace_index = rest_api.binaryMediaTypes.index(path_value)
                    fixed_patch_ops.append(
                        {"op": "remove", "path": f"{binary_media_types_path}/{replace_index}"}
                    )
                    patch_op["op"] = "add"
            elif patch_op_path == "/minimumCompressionSize":
                if patch_op["op"] != "replace":
                    raise BadRequestException(
                        "Invalid patch operation specified. Must be 'add'|'remove'|'replace'"
                    )
                try:
                    
                    value = int(val) if (val := patch_op.get("value")) else None
                except ValueError:
                    raise BadRequestException(
                        "Invalid minimum compression size, must be between 0 and 10485760"
                    )
                if value is not None and (value < 0 or value > 10485760):
                    raise BadRequestException(
                        "Invalid minimum compression size, must be between 0 and 10485760"
                    )
                patch_op["value"] = value
            fixed_patch_ops.append(patch_op)
        _patch_api_gateway_entity(rest_api, fixed_patch_ops)
        
        endpoint_configs = rest_api.endpoint_configuration or {}