basically like it's done on windows
make sure your gfx drivers are good (other games, glxgears work etc)
install linux-native steam
login to steam
install GTFO
launch GTFO, make sure it launches and works okay
if "not responding" after trying to start a level, try x11 instead of wayland (on ubuntu you log out, select user, on password screen you go bottom right of screen gears -> ubuntu on xorg)
download r2modman for your distro from https://github.com/ebkr/r2modmanPlus/releases
launch r2modman, select GTFO, should detect your GTFO directory, can be set from settings if not
create a profile, install the mods you want in it
click on launch modded, modded launches, enjoy
Tested to work with r2modman 3.1.34, earlier versions needed some extra steps to launch modded properly (like creating a bat-file to launch modded and a doorstop_config.ini file with a full path to the BepInEx.Unity.IL2CPP.dll file etc)