https://bugs.winehq.org/show_bug.cgi?id=56026
--- Comment #3 from alexandros.frantzis@collabora.com --- Thanks, in that case the https://gitlab.winehq.org/wine/wine/-/merge_requests/4695 MR should fix the side buttons (4-5) for you.
You also mention mouse3 (=scroll button click, I assume the same as middle click?). Does that not work for you?