at first the game would not spawn a window, and exits immediately, regardless of the proton-version. However, starting the game manually from the CLI with either flatpak run com.valvesoftware.Steam steam://rungameid/1659420 or steam steam://rungameid/1659420 (depending on how you installed steam) led to the precaching of vulkan-shaders and finally the start of the game. After this first start, the game also launched from the regular run-Button.