The game doesn't launch because of EA App crashing on start.

Because of that you need to install Origin first on a The Sims 4 prefix from the link on https://github.com/p0358/Fuck_off_EA_App - the easiest way to install it is to replace The Sims 4/__Installer/Origin/redist/internal/EAappInstaller.exe with Origin installer file.

After that, get the FOEA patch installer from the same link as above and install it while checking the "Pretend EA App is installed" option. (Just so you won't have a further problem of Steam trying to run EA App installer)

At the end, put the launch options command and you should be able to run The Sims 4 fine.

In short, EA doesn't like Linux players.