Surprisingly, Rockstar have now added BattlEye anti-cheat to Grand Theft Auto V / GTA Online, and sadly it seems they have not enabled the support for Linux desktop and Steam Deck with Valve's Proton. ARTICLE UPDATED.
This game has such trash net code. It's surprising they won't fix it considering how much cash they're milking from it. But I guess it's cheaper to lose players than to make it better for everyone..