"While that is a cheap, likely from China, so anything is possible the changing light depending on the state of charge tells me there is definitely a charge controller in there. "
Confirming that by subsequent observation of behavior.
One thing I didn't think of right away is that charging from the computer USB port stops when I hibernate it or shut it down, although the fan itself doesn't stop since it's running off the battery at that point.
Duh.

One of those "obvious in hindsight" things.
No problem, I used to have to manually shut off the previous noisy 110V fan anyhow.
Terry