I've tried multiple different 2 and 3 click options in BTT, tried w suggested profile below, didn't work, then tried adding a preset for taps, another for clicks (as someone else suggested) then had all presets triggered by option key, restarted BTT, and again nothing happens, no behaviour from normal 3-finger for either taps or clicks (working fine after enabling middle-click on non apple mouse in BTT, btw).
The preset you linked still works fine in general. However the system three finger dragging breaks a lot of things in BTT because it changes the fundamental behavior of the trackpad, maybe it's causing issues with this as well.
Or maybe it's just a misunderstanding on how the preset works? Basically you need to click with three fingers, then remove two of the three fingers and move the remaining finger to drag.