There are lots of books that explore immortality outside the context of society. Either they live alone or in a heaven/palace of one sort or another, or they drift from place to place to avoid recognition, or something of the sort.
What I'm interested in, and may write about, is a godlike being that likes people and visibly hangs out in society, but has zero interest in political or religious power.
Unlike this question, I'm only asking about a single individual with absolute immortality of the also-invincible variety, and rarely-used magical powers along the lines of deities in most mythologies. Unlike Superman, this individual has no overwhelming compunction to stop crime, solve people's problems, or impose their will on/act for the major benefit of others in any similar way. Magic is unavailable to any other member of society. Everything else is basically Earth-analogue.
For the sake of specificity, this being has enough power to be an Out of Context Problem for even a modern society, looks fairly unremarkable compared to the locals when not using its powers, is fairly humble and likable, has no patience for politics, doesn't give commandments even when asked, has been around at basically the same address under basically the same name for the last 5,000-10,000 years, and likes chess games with strangers, watching TV, and going to parties.
How would this sort of creature inadvertently affect the structure of society?
Edit: This being has a perfect memory, but only tells stories that they personally consider fun or interesting. The entity is a big fan of any social activity such as dance, games, and media of all kinds. They are mostly uninterested in serious research, creating their own works or deep inquiry. Their main hobby is just interacting with and meeting people.