We don't know specifically what they can do, but we do know that they are still highly limited.
No. We know that they WERE highly limited in prior editions, if you even used those rules, since stats for the gods were not in the core. Your concept of limitations does not hold for any games but your own.
5e has this "rulings not rules" thing going. And 5e has no rules about such powers to begin with. So, really, in a 5e game, they can and will be whatever the folks in the game want. And they are not somehow wrong for doing so just because you say otherwise.
The real question is: Will it be fun for your group if Entity Type X can do this?