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.
Breaking Linux support after-the-fact ought to be grounds for a full refund (no matter how much time or hours of play have passed). Valve ought to allow such refunds and forcibly debit Rockstar's Steam publisher account, whether Rockstar likes it or not.
Same thing happened for the whole Bioshock series. They rolled out the update just over 2 weeks after a big sale so it was beyond the standard refund policy too.
Update #1 - 14:31 UTC: Rockstar have now put up an official FAQ for BattlEye where they state:
Is BattlEye compatible with Steam Deck?
Steam Deck does not support BattlEye for GTA Online. You will be able to play GTAV Story Mode but unable to play GTA Online.
Note: GTAV and GTA Online are not officially supported on Steam Deck and all technical support questions should be directed to Valve’s Steam Deck support content and community.
I'm still currently waiting for an official statement from Rockstar on any plans to enable it, since BattlEye as mentioned below is supported on Linux / Steam Deck.
So I wonder what my copy from rockstar will do now, it worked like a week ago under wine(single player). I bought it before it was available on steam unfortunately.
That said gta online was never good so idgaf about that part but Battle eye isnt going to do shit so sucks for those that do care.