JKR 'uses' quite a few folklore and myths, but never really goes into any depth with them. It's all very surface level, that's why fairies are depicted like little glowing Tinkerbells rather than the powerful, chaotic, unknowable, and all-around strange creatures they are in folklore. If you expect her to have any depth in what she does, you're going to be sadly mistaken.
Edit: If you want a story which truly does go deep into the myths and folklore it draws upon, I recommend Jonathan Strange & Mr Norrell, by Susanna Clarke.
The best fantasy book I ever read was Jonathan Strange & Mr. Norrell. It's a slow burn, but the world building is second to none. There was a BBC miniseries as well. I haven't watched it but it's well-reviewed.
Some others I really like:
Hoity toity literature: Moby Dick (way more fun than it's reputation lets on), Notes From the Underground by Dostoevsky.
Non-fiction: The Devil in the White City by Erik Larson (chronicles the building of the World's Fair in Chicago alongside HH Holmes building his Murder Castle), The Emperor of All Maladies by Siddartha Mukherjee (history of cancer).
Great sci-fi: Dune, Canticle for Leibowitz, Fahrenheit 451.
Books that are really fun to read: Anything by Neil Gaiman, Dresden Files series.
It just got turned into a tv show, but I haven't seen it yet. It is NOT like Harry Potter. It's much closer to Master and Commander, but with magic.
Try Susannah Clarke's Jonathan Strange & Mr Norrell.
Very Good Omens.
‘Jonathan Strange and Mr. Norrell’ by Susanna Clarke. It’s not horror, but I think you will still appreciate reading about the exploits of these two great magicians.
https://www.amazon.ca/Jonathan-Strange-Mr-Norrell-Novel/dp/0765356155
<strong>Jonathan Strange & Mr Norrell BBC TV Series Episode Guide</strong>
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>That would be like the military paying wizards