I've never experienced anything like this, across multiple different Linux systems and various Source games. Am currently on Arch as well, using Proton Experimental, and have been playing Apex on it for around a year with no specific issues.
Are you using libinput (Wayland), xinput (X11), or something else (ie gnome-tweaks) to manage your mouse? Here's an Arch wiki page about mouse acceleration that may be relevant. What you're describing is definitely not normal behavior, and it makes me think that your dpi settings may be different between operating systems, or that your prefix has something configured weirdly. An issue may need to be raised with the Proton team, if not.
