For anyone who is interested, I did a little digging.
Someone in our house is a fan. They got an “army bomb” in preparation for a show in the US that ended up being cancelled due to COVID-19. I’m not allowed to disassemble it, but I was able to look at the label in the battery compartment and get the FCC ID and find their certification info.
For some reason the internal photos are embargoed until 10/11, despite the thing being in the wild. However, the test report reveals that it uses…BLE, which I already knew. It doesn’t seem to have another radio, though. I did find internal photos for a similar device, registered in 2016, from the same manufacturer. The markings on the bluetooth SoC aren’t legible in the photos, unfortunately.
I can’t find any real teardowns, but one fan took hers apart. No closeups, but its clear there isn’t an IR receiver anywhere IR could be received.
The company that makes the devices is Fanlight, which I can’t link to because I’m a new user and I’ve already made too many links.