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7 days ago20 hours in without a hitch* and loving the game. Bazzite with a 4090.
Regarding your issue, Steam automatically installed the BattleEye runtime for me before it installed the game but I have seen reports on ProtonDB of some folk needing to install it themselves. Not sure how to do that, but maybe a game reinstall would force it.
* Well, first time I booted it up the game erroneously complained my Gen 5 NVMe was too slow. But that message hasn’t come back and it hasn’t stopped me or impacted performance.
Good luck, see you on the sands!