Currently the side mouse buttons act like the middle mouse button. They are treated like forward and back in Chrome and Firefox. I think this configuration is most logical. However, Safari has the same behavior as Orion.
Similar to this bug in Firefox that was fixed a few months ago:
https://bugzilla.mozilla.org/show_bug.cgi?id=1615213
Alternatively for now you can use SideButtons on github, which is a light application which simply makes them do three-swipe gestures backwards and forwards logically, so that in most applications it will go backwards and forwards. Which are the mouse 4 and mouse 5 buttons respectively.
I also support this suggestion to be implemented natively in the browser. Though I also appreciate the suggestion from @Fortrikka as alternative, but moving forward in the future most users will also have the same expectation with the mouse forward/back buttons to work as-is.
I used the Side Button Enabler apps but the annoying thing is that they are Intel builds only. It's the only app on my setup that requires Rosetta, which is quite a big dependency just to get a mouse back button working.
Glad to see that this is coming soon.
Just realized that the side buttons on my mouse replicates a left click in the browser. It would be nice if there was support for those buttons to move forward/back pages and possibly through tabs with the control/cmd keys
