How to check mouse button 4 and 5 remapping
Select the physical button you intend to test, press it over the test area and compare the received code with the expected one. A driver can intentionally map a side button to another browser button or keep it as a macro that the page cannot see.
Run the same sequence after switching profiles, disabling remapping software and trying a second browser. This isolates a browser-visible mapping issue from a dead switch or an input that is reserved by the operating system.