Depends on what gets rotated, I see these lines tell us the $Neck and $Neck/Camera get rotated.
head.rotate_y(-event.relative.x * sensitvity)
camera.rotate_x(-event.relative.y * sensitvity)
Looking at your video again the weapons do move side-to-side (with the $Neck) and up-and-down (with the $Neck/Camera) so they must be children of camera.
If the arms only synchronize up/down then add the $Neck rotation to the synchronizer. if the arms do not move at all then it is a synchronizer issue, maybe the multiplayer authority isn’t being assigned correctly? I highly doubt it’s a synchronizer issue as it worked in the first video.