Yes, sadly I too can confirm, this new security feature is not currently compatible with BattleEye.
According to BattleEye they did say they “working on finding a solution and are also in contact with Microsoft regarding this issue, unfortunately there is no easy or immediate fix for it.”
BattleEye FAQ
Could some moderator please sticky this post or repost this information as it’s likely to impact a lot of players running Windows 11?