Celebrim
Legend
You've already touched on this somewhat, but to add to what @Charlaquin said about D&D being largely written lately by people with little background in religion, most ancient societies defined "gods" rather more loosely than we would to today where "god" means something like the Abrahamic god. Gods in my campaign world, the divine rank things that have clerics, all have an origin story as being produced from fruit of the tree of life ("Yggdrasil") or else offspring of the couplings of those beings. But underneath them are a great host of created and uncreated spirits down to the level of things like sprites which are often worshipped (and relate to Shamans rather than Clerics), and for that animistic portion of my worlds cosmology I draw heavily on Celtic, Japanese, and Edo and other West African myths. These are the "small gods" or kami in in Shinto terms, or nymphs and similar "gods" in Greek terms and at the top level they shade off into figures that seem divine from the perspective of a typical mortal.
While major deities like Showna and Aravar played background roles in my last campaign, spirits of that level from Slaad Lords of Chaos, to the Archangel of Fire, to the Secundus of Submission, to Earth Spirits with global scope, to Ulgrick the Devourer, to the Prince of Cats are also flitting around the PC's lives in various ways. The Shaman at one point got to meet the earthly form of one of her spirit patrons. And beyond that, one PC is haunted by the ghost of a woman he accidentally murdered, and for a while another was being fed on by a type of fairy that bewitches men and lives off their body heat - hypothermia while in the jungle. And all of those things are in some way "kami" in the Japanese sense or "gods" in the Greek sense of the word. The fairy was the "god" of a particular sulphureous hot spring, for example.
My point is that you don't have to drop Zeus or the equivalent into the campaign to make the divine or spiritual world important to it, and Ghibli's work is an excellent example of having a world haunted by powerful spirits in a way that is more closely grounded with ancient religion than the average D&D writer.
