I'm on Catalina 10.15.3 using a Magic Mouse. The current option to disable single finger horizontal scrolling works. But I often accidentally scroll horizontally when I inadvertantly swipe with two fingers. I've tried everything I can think of (e.g., assigning "no action" to a two finger left and right swipe) but nothing works.
A competitor's product, the Multitouch app available at https://multitouch.app/, has an option to disable all horizontal scrolling (including two finger) so it does the trick. If Multitouch can do it, it seems to me that BTT ought to be able to do it.