The biblical plot ended with season 5. I used to find it equally annoying but upon re-watching (I will neither confirm nor deny that I’m in my fifth run-through of the whole series) seasons 4 & 5 are actually pretty good.
They use the biblical elements from more of an historical perspective to drive some interesting new plot directions (I mean if you have demons/hell, there’s gotta be a heaven, right?) rather than overly religious. It’s clear that they’re not pushing a religious agenda one way or the other though (angels being dicks, for example) and there are some pretty great episodes in there.
PLUS Lucifer and Death are two of the best side characters they’ve ever created, and that’s all season 5.