Creating A World With Hands-Off Deities?

[Bohandas]

But could a cosmology be created that turns the triangle into a rectangle, with a setting where the gods do not grant spells or answer individual prayers, but are still indisputably present in the world such that people believe in them and worship them?

Definitely.

One possible example would be an apocalyptic cthulhu mythos setting set after the great old ones reawaken.

(although it would not necessarily need to be a grimdark setting like the cthulhu mythos; this is just an easy example)