An example of a non-coding "asynchronous agent" in my mind is something like deep research. It runs for a while in ChatGPT or Gemini, and when it's done, it produces a markdown file or google doc with its findings. The parallel with your definition of "asynchronous coding agent" is that I'm not watching it work or involved in the process.

But your last point highlights exactly why the sync/async distinction doesn't hold up as a binary classification. Even with deep research, I go back and forth on a plan synchronously before sending it off to run async. Any good asynchronous coding agent should work the same way.