### 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_
if self.forward_url.hostname:
            forward_host = self.forward_url.scheme + "://" + self.forward_url.netloc
        else:
            forward_host = host
        forward_path_root = self.forward_url.path
        forward_path = path[len(self.base_url.path) :]  
        
        if forward_path and not forward_path_root.endswith("/"):
            if not forward_path.startswith("/"):
                forward_path = "/" + forward_path
        forward_url = forward_host + forward_path_root + forward_path
        return urlparse(forward_url)
class EndpointProxy(ProxyListener):