I don't think we want to provide a separate API to access the task handle from here; if we allow you to get a task handle for the current task, you can capture that in the closure instead. If we don't allow you to get a task handle for the current task, we shouldn't have this API either. Either way, this extension is something that we should consider as part of Structured Concurrency. Joe's proposal is more of an extension of async/await than a part of Structured Concurrency.
Doug