Nano Dimmer itself is compatible to fan loads, but it has been found that fans have a specific way to set its speed. For most cases the Fan is not compatible to the method of dimming Nano Dimmer provides. Nano Dimmer adjust the voltage level for dimming, while Fan loads often time uses a specific 3 part setting that are suppose to be set to these settings, these types of fan are not compatible to Nano Dimmer which the fan would generate a buzzing noise that can damage the fan leaving the fan motor to permanently generate this buzzing noise.
You will need to ensure that you have a Fan load that adjust its speed to the amount of voltage instead of 3 set speeds. In this case, i can confirm that your Ceiling fan currently is not compatible to Nano Dimmer as it uses a 3 speed setting.
The fan load type that is compatible to Nano Dimmer is a "Electronic Fan Regulator" which is a TRIAC based dim setting for Fans, you can find more information here: https://www.bijlibachao.com/fans/choose-the-right-regulator-for-ceiling-fan-for-electricity-saving.html
Most fans used often see have issues with is the conventional type fan which will work to some extent with Nano Dimmer, but can damage the conventional type fan. For the conventional type fan, we would advise using Nano Switch for ON/OFF control only.