I’ll second the onboard storage, and add that any >3-button mouse should have buttons that map to actual key/character presses. I got a Razer Basilisk Pro on clearance, and it does have onboard storage, so once I turned off the RGB in the windows software on an old laptop, I could get rid of it. What I didn’t realize til later is that the nice little thumb lever can’t be remapped by anything but the Razer software (which has to be running all the time) because it doesnt register as any key combo, it had to be processed through their app to be used. Damn it.
Edit: Have you tried looking at what keycodes the side buttons on your current mouse are mapped to? Sometimes you can intercept that input and make it perform correctly. I haven’t done it on linux yet, but I’m sure there’s an equivalent to AutoHotkey for Linux.