The bug
It is not possible to bind any in-game actions to the act of moving the scroll wheel up or down, unlike with other mouse button inputs.
Rebindability would be expected due to the existence of scrolling in the hotbar (MC-268283).
How to reproduce
Enter they Key Binds menu
Click on a control to rebind it
Scroll up or down
Expected results
The game control in question would become bound to this specific movement of the scroll wheel.
Actual results
It is not.
Further notes
I do not have a mouse with a horizontal scroll wheel (e.g. A4Tech 4D, Logitech MX Master, and so on), however I believe horizontal scrolling to be affected in much the same way.
Linked issues
relates to
Comments

This is a feature request. Please leave feedback on feedback.mincraft.net
So.. It seems like this wheel should switch inventory slots, isn't it?