As far as paladins goes, 5e does exactly that. Their power doesn't arise from deities or religions beyond the specific tenets of their Sacred Oaths.
For settings, I can't think of one that did exactly what you're saying here. They still have gods with spins, or delete clerics.
— Dan Dillon (@Dan_Dillon_1) February 18, 2022
Some settings I'm not familiar enough with to speak to directly that might fit your bill:
Red Steel
Birthright
Jakandor— Dan Dillon (@Dan_Dillon_1) February 18, 2022
Dark Sun