Using wev (wayland event viewer, which shows pressed keys) the side buttons show up as extra mouse buttons, so it should be possible to remap them.

button: 272 (left)
button: 273 (right)
button: 274 (middle)
button: 275 (side) <- side button
button: 276 (extra)  <- side button

PS: My old Logitech G710+ keyboard has some extra buttons which show up as normal numbers, which makes them pretty much useless. A while ago I found the now abandoned sidewinderd project which adds support for them. It's sad that those manufacturers don't create proper standards for these kind of things and instead hack it together somehow.