Story mode should be playable, there is a option to disable BattlEye in Rockstar Launcher
https://support.rockstargames.com/articles/33490543992467/Grand-Theft-Auto-Online-BattlEye-FAQ
Steam Deck does not support BattlEye for GTA Online
Such a crappy way of wording it and trying to blame the steam deck when BattlEye has said that they have had linux and wine support long before the steam deck came out
Official Rockstar Community (RP) Servers will not require BattlEye to play. Community Server launchers will disable BattlEye as part of their launch processes.
What makes RP servers so special that they don’t need BattlEye?
https://www.pcgamer.com/battleye-anti-cheat-confirms-steam-deck-support/
BattlEye has provided native Linux and Mac support for a long time and we can announce that we will also support the upcoming Steam Deck (Proton). This will be done on an opt-in basis with game developers choosing whether they want to allow it or not.
You don’t build an OS for an application, you build an application for an OS. It should read “BattlEye doesn’t support Steam Deck”.