Returns the current processing state of a task.

While the task is running, returns status: processing with any stream events flushed since the last poll.

Once the session completes, returns status: completed with result.message_id pointing to the final message.

The completed result is consumed on first read and is held for at most 2 hours after completion — subsequent polls return 404, so persist the result on first successful read. If you miss the result window or have already consumed it, fetch the persisted history via GET /tasks/{taskId}/messages instead.