### 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_
return os.path.join(config.dirs.cache, SERVER_CERT_PEM_FILE)
def start_proxy_server(
    port,
    bind_address: Union[str, List[str]] = None,
    forward_url=None,
    use_ssl=None,
    update_listener: Optional[Union[ProxyListener, List[ProxyListener]]] = None,
    quiet=False,
    asynchronous=True,
    check_port=True,
    max_content_length: int = None,
    send_timeout: int = None,
):
    if bind_address:
        bind_addresses = bind_address if isinstance(bind_address, List) else [bind_address]
    else:
        bind_addresses = [BIND_HOST]
    if update_listener is None:
        listeners = []
    elif isinstance(update_listener, list):
        listeners = update_listener
    else:
        listeners = [update_listener]
    def handler(request, data):