Because the client does shutdown work in a background async thread, the larger context has no way to block until shutdown is actually complete; this can cause issues like HELP-42442, where the calling context is invalidated while that background work is ongoing.

To support this, we should provide a blocking (non-async) client method to wait on final shutdown; it can be implemented via a one-shot channel that the worker thread(s) post on as the final pre-drop action.