On my G502 Logitech mouse my mouse 3, 4 and 5 all register as L Shift and i don’t know why. I fix it by verifying the game. Don’t know if its on your end or mine. just an fyi
Have you mapped the mouse through the logitech software? I know i had to originally set mine up to use either keyboard binds, macros or the original "mouse button 4 through 11
Button mapping worked perfectly fine for me using a G502 Proteus. I don’t use any driver software, either, just the default Windows 10 plug-and-play driver. Sorry I can’t help you.