How could I control a ceiling fan that receives constant power with a Caseta Pico switch?

Where this came from: this question was asked on r/homeautomation — not here. We answered it there, in public, and this is that answer.

There's no Caseta canopy module. Lutron's only fan device in that line is the wall-box speed control (PD-FSQN-WH), and it needs a box, a hot, and a neutral. So with constant power and no switch leg, you've got two real paths.

Path one, the one I'd pick if you're staying in the house: have an electrician fish a cable to a new wall box so the fan is on a switch leg, then put the PD-FSQN-WH in the box and pop a Pico on the wall next to it. That gets you four speeds, a Pico that works even if your internet is down, and no hub in the middle. Two caveats that trip people up: the fan's pull chain has to be set to high and left there, and if the fan already has an RF receiver in the canopy you have to pull that receiver out first, because chopping the waveform upstream of a receiver is how you cook it. That control is also intended for AC motors. If you've got a DC-motor fan with an integral controller, this whole path is off the table and you should tell me the model before you buy anything.

Path two, no wire pulling: put a universal fan remote receiver in the canopy if the fan doesn't already have one, then a Bond Bridge to learn its RF or IR commands. That gives you app and voice control immediately. The catch is the Pico. A Pico is Lutron Clear Connect RF and talks to Lutron gear only, so to make a Pico press turn into a Bond command you need a Caseta Smart Bridge plus something doing the logic in between, Home Assistant or Hubitat being the usual two. That's three boxes to control a fan, which is why I don't love it, but it works and it doesn't involve an electrician. I've seen it claimed that one of the Bond bridge models can take a Pico directly without the Lutron bridge. I haven't done it myself, so verify that with Bond before you buy on the strength of it.

Honestly, if you only want the pull chains gone and you don't specifically care that it's a Pico, path two without any Lutron in it at all is the cheap answer, maybe a hundred bucks a fan. The Pico requirement is what adds the bridge and the hub.

If you post the fan's make and model, or a photo of the canopy with the cover dropped, I'll tell you which path that particular fan supports and whether it's already got a receiver in there. Free, no catch. I'm a Lutron dealer and have been since 1999, and I do Lutron and Control4 work remotely for a living, so take the Lutron enthusiasm with that in mind.