small update - there's been a minor (17.4 MiB) patch to Apex since. Could be worth checking in with it to see if it has resolved linux compat,
Edit - it's working for me on Fedora 40 Workstation. NB that I've never hit the original anticheat issue to begin with, and I use the following launch command to run the game under VKD3D (mostly AoT shader compilation) along with suppressing launch splash screens / videos and presenting Mangohud