Fabric, 1.20.1, Controllable 0.20.2
Mod used to test this: Marium's souslike weaponry.

This mod has weapons that use special abilities as part of their normal attack. When clicking left click(standard attack button) with mouse the ability spawns as expected. When using controllable and hitting right trigger which is the bind set for Attack/Destroy the ability does not work and it is just a standard swing.

I checked keybinds for the mod and none are additional binds associated with left click for mouse. My guess is that it is seeing some form of input with left mouse click that controllable is not generating with it's own bind.