Got the switches and installed them in a couple of bathrooms. They show up as lights in Home Assistant, but that’s a known problem.
Using an ancient builder-grade AirKing, it works just fine.
Using Panasonic WhisperGreen FV-0511VK2, it works. Once. After you turn it off, it does not start again, until you cut the power at the breaker. Swapping back the old dumb switch, it works.
Note that Panasonic WhisperGreen FV-0511VK2 has a “delayed start” feature built-in that can’t be changed. Once I turn it on from the dumb switch, it takes 10 seconds or so to start.