The challenge with "extra button" mice and keyboards is that those key inputs are generally only recognized by the device's driver, before being forwarded as a keystroke/click/event that the OS can recognize.
While a lot of applications support Mouse Button 1-3, and often 4/5, anything beyond that is not part of any interface standard; similar limitations exist with keyboards that have macro keys, too.
The workaround for this is generally to map those buttons to a function the OS can recognize, such as an existing key or button. An example of this would be binding "Mouse Button 26" to "s" so that both S on the keyboard and MB26 trigger the search box. If you were to unbind S from Search, MB26 would stop working, too, since you're now just mimicking an unbound hotkey.
Logitech Options software supports creating a custom profile for any executable, so you should be able to set up a highly customized set of mouse-based shortcuts, without impacting any non-Fusion workflows.
Lance Carocci
Fusion QA for UI Framework/Cloud Workflows, and fervent cat enthusiast