For lowest power, the LePotato is (humorously) named for it’s low power requirements, and I understand the Pi Zero can actually run for hours on small rechargeable battery packs.

A smaller lower power draw Pi Zero alternative that comes to mind is Arduino Teensy. But it sounds like no one is running Linux on Arduino Teensy, yet ?

But the folks in that forum sound like the types who might make it happen at some point.