I haven't seen much interaction with the gods aside from the Selune temples and the Absolute the Goblins worship.
Could you setup something similar to the background story enhancements? I would also like it taken a step further, by getting blessings from your God that grant you abilities (like DOS2) depending which God you worship. This should have a huge impact on classes like the Paladin or Cleric but also the less divine classes if they perform actions aligning with their God. This would be great in terms of moving from a righteous paladin to fallen paladin, and give options for restoring favour with their God. It would allow something similar to a multi class where a wizard would typically worship Mystra, goddess of Magic, but maybe decides to worship Cyric instead to focus on necromamcy, or Tempus the God of War if they want to the ability to avoid being frightened or granting courage to allies.
It would be cool if there was a choice of options during a short rest that would impact either the class, background, divine development and restrict the recovery based on the selection. It would allow the player a deeper interaction with their character and build an understanding of where they are heading.
Hope these suggestions help!
