This should generally work for games of various origins as well.
Extra mouse buttons should generally map correctly. For me, my Logitech MX Master 3 works under Arch. You may need to add udev rules if your mouse generally works but additional buttons don't seem bindable.
Try an Arch linux based distro, Omarchy or Manjaro. Most of these tweaky things will generally work better since you will be on the latest versions of software.