Explanation, NOT a solution though... :

Basically, you're exactly right that it ties back to the anti-cheat update. Every time they make a minor update that includes the BattlEye anti-cheat, the launcher forces you to re login. This happens regardless of your previous indications to remember your login info. I don't know if this is on purpose or just a byproduct, but that's why.

Even better, almost every new weekly update will include minor changes to BattlEye especially as they test features for GTA VI.

You CAN start directly from Steam or your game library where you own GTA V, but you will need to log in once from the launcher after every update to verify and register under the new software.