When speedrunning, people often rebind the scroll wheel to the portal 2 Jump action, in order to BHop effectively. I was wondering if it was permitted (or banned) to use extra mouse buttons for the same purpose? It says "no scripting" in the Game rules, but would this violate that rule? Just curious.

if you mean binding a side mouse button to +jump, it's allowed
(or any other action, as long as you only use 1 action on 1 bind)

So that would be a no for using the button to bhop, as that would require a spam input.

Binding the jump action to your mouse wheel is accepted, pretty much every speedrunner uses it because you can't really bhop effectively and consistently using a keyboard key

you can bind jump to a mouse button, but as Evandar said mouse wheel is better