Typically you won’t see much for controlling the fan unless you’ve written custom apps, like the one below (old, but maybe still works?)
What I’ve done is create virtual for each of my thermostats’ fans, and I use my own custom device handler for my thermostat where I define how ON/OFF controls the fan. I then use Smart Lighting to link the thermostat fan to the virtual switch for the fan. When the virtual switch is turned on, the thermostat fan turns on, and visa versa.
The nice part about this configuration is that the virtual switches are discoverable by Alexa, and then can be controlled. Also, these virtual switches can be used in any Routine or Scene.