Side mouse buttons should function as the back and foward buttons. Firefox is able to do this.
Try MiscHorizontalWheelNavigates=TRUE in your ~/.config/Thunar/thunarrc (see docs/README.thunarrc for details about hidden options).
That works. Perhaps that should be the default setting?
It was the default, but people with weird integrated laptop touchpads/mices complained that it was too easy to accidently change folder, so it's disabled by default.