Kaeya and Diluc backstory spoilers!!
Is it just me, or was Kaeya breaking the news to Diluc on the day his dad died one of the nicer things he could've done? Allow me to elaborate:
If he had decided to tell Diluc he was a spy later on, then he would've been hurt twice. However, what Kaeya did was rip the band-aid off. Prolonging the bad news might have made things worse between them too, because he'd be keeping that secret for that much longer.
However, by telling him on that day, now Diluc has had one really, really bad day instead of two. Sounds insignificant, but would you prefer to have moderate amount of bad luck for a week or a lot of bad luck for a day? Most people go with the second one, and that's what Kaeya did. If I were in Kaeya's position, I can't say I wouldn't do the same thing. This made it easier for Diluc to recover as well, most likely.
So maybe, he isn't as stupid as people thought.
Maybe he did this on purpose, trying to protect his brother one last time.