### 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_
method: str = None,
    path: str = None,
    data_bytes: bytes = None,
    headers: Headers = None,
    forward_base_url: str = None,
    listeners: List[ProxyListener] = None,
    client_address: str = None,
    server_address: str = None,
):
    """This is the central function that coordinates the incoming/outgoing messages
    with the proxy listeners (message interceptors)."""
    from localstack.services.edge import ProxyListenerEdge
    
    if (
        not config.DISABLE_CORS_CHECKS
        and should_enforce_self_managed_service(method, path, headers, data_bytes)
        and not is_cors_origin_allowed(headers)
    ):
        LOG.info(
            "Blocked CORS request from forbidden origin %s",
            headers.get("origin") or headers.get("referer"),
        )
        return cors_error_response()
    listeners = [lis for lis in listeners or [] if lis]
    default_listeners = list(ProxyListener.DEFAULT_LISTENERS)
    
    
    is_edge_request = [lis for lis in listeners if isinstance(lis, ProxyListenerEdge)]
    if is_edge_request:
        default_listeners = [