### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Authorization headers being sent to API gateway are received on lambdas as "empty string"

### Expected Behavior

_No response_

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

Run a API Gateway with lambda integration

### Environment

```markdown
- OS:
- LocalStack:
```


### Anything else?

_No response_
parsed_url = urlparse(request.url)
        path_with_params = get_full_raw_path(request)
        method = request.method
        headers = request.headers
        headers[HEADER_LOCALSTACK_REQUEST_URL] = str(request.url)
        headers[HEADER_LOCALSTACK_AUTHORIZATION] = headers.get("Authorization", "")
        return modify_and_forward(
            method=method,
            path=path_with_params,
            data_bytes=data,
            headers=headers,
            forward_base_url=forward_url,
            listeners=listeners,