I have one as well in the same situation with a pull chain but a light switch on the wall for built-in lights in ths unit. It also had a second chain for the lights but left that turned on at the fixture and removed the chain so the lights are controlled by a Shelly Dimmer 2 behind a momentary wall switch (replacing a dimmer switch) programmed for down=off, hold down=dim, up=on, hold up=brighten (a total PITA but a very specific use case, here. But I digress…
My pull switch for the fan is the typical, per pull, off-low-med-hi-off sort of thing. I have asked in the forums if anyone had any ideas for getting a Shelly relay to work with the fan but they suggested using three separate relays, one for each of those speeds. I don’t like that idea… so although the way I control those lights is elegant, it might be a cleaner solution to just replace the fan altogether with something smart that can interface with HA… but I need one with lights as well… !