Human mythology usually talks very little about how non-humans live
Exactly! It is more about how they interact with us. Like swapping children for changelings or living under your house. Sitting on your chest while you are trying to sleep. Leading travellers astray in the woods. Whatever. They usually get the blame for something. Or explain strange things that happen.
Elfs in particular are stated to be small and mischievous, playing pranks and being cruel to humans. I would nowadays call those creatures pixies or at least fairies, because of the prevalence of Tolkien inspired elfs capturing the word.
They are not barbarians, that’s more of an orc trope. They are often the most “civilized” race in the setting
Yes. So much civilized that they gave up on "civilisation" and returned to nature to live in harmony with it. At least the wiki on generic elves does mention this notion whose key traits are being friendly with nature and animals.
I do not know exactly how and where it was popularized. Seems a bit like the pointy ears. Those got longer and longer over time, so now Elves have very long pointy ears, so people know they are elves.
So, just like people think of a generic barbarian, if you say "orc", people will think of a generic woodlands ranger and assume a wood-elf, if you say "elf". Unless of course you prepare the setting.