This idea came from an old video game called mortal kombat, which introduces a very long lived human race that existed in a realm bordering earth. The one it focuses on is a woman who is ten thousand years old, but is regarded as young by her people. Not much is expanded on their culture, and they seemed to be very "human like" for a people with their lifespan. So i tried to imagine what their society would be like.
Gods are vastly powerful beings that represent the pinnacle of the human race. They have a lifespan of 40,000 years and live in a parallel reality that exists side by side with the mortal realm. These gods adhere to a prime directive that was given to them by the universe, which is their creator. The directive tasks them with protecting humanity from threats originating outside reality. They retain their individualism, and have their own personality and egos. However, this directive is superimposed on them, as it is a part of their nature that they cannot turn against. It is helpful to think of them as sentient, self aware programs, or defense mechanisms of the universe itself. Gods view the universe as a larger cosmic entity that they are apart of rather than existing separately from it. They have emotions and experience their full range, but have evolved a very practical mindset. logical solutions take precedent in making decisions. While the gods "love" humanity, they tend to see them as a unit more than individuals, or as part of a bigger whole. This is due to their partial mindset and outlook on reality.
These gods are constantly at war with otherworldly creatures that exist outside of reality and threaten the mortal realm, such as demons, eldritch abominations, and the like. As such, their culture revolves around social order and cohesion, with everyone working towards a common goal. Males are usually the ones sent off to war and fight since they are more "expendable". Females are left behind to run things and keep the world functioning (making sure the sun rises and sets, seasons change, etc). God's don't breed very often, with a woman''s reproductive cycle taking place every 1000 years. They also don't interact with humanity very often, being busy defending it against enemies and running creation from behind the scenes, and seeing one is a big enough event in a human''s life to be memorable.
Included in the directive are a set of cosmic rules that a god abides by. These rules are meant to protect humans for abuse, but are left somewhat open-ended and flexible to situations.
Gods can't harm mortals, unless it's done for self-defence or the greater good (So they can smite a cult that wants to summon cosmic horrors, but can't destroy settlements because of a slight).
Gods must always act in the best interest of humanity and the material plane (adopting an utilitarian philosophy).
Gods are allowed to directly manifest on the material plane only if absolutely needed.
Granting powers and offering guidance to mortals is allowed, but only if these mortals act for the greater good.
Based on this setup, what influence would this race of God's have over humanity? How would they wield this influence?