I was looking for exactly this kind of thing a while ago and ended up down a deep rabbit hole. Holly Black's 'The Cruel Prince' is almost a mandatory starting point, but the political angle there feels very 'courtly' to me—lots of backstabbing over status and favor, wrapped up in Jude's mortal-in-Faerie perspective. It's sharp and personal. For something with a different texture, 'An Enchantment of Ravens' by Margaret Rogerson handles fae politics through the lens of craft and artistic value; who has the right to create, and what that power means, becomes a kind of intrigue in itself.
Then you've got the urban fantasy side, like Seanan McGuire's October Daye series. Toby's constantly navigating the layered courts of the San Francisco Bay Area—the political stakes are life-and-death, but also deeply entangled with old laws and debts. It feels less like a chess game and more like walking through a minefield of etiquette. For a darker, more monarchical struggle, Sarah J. Maas's 'A Court of Thorns and Roses' series, especially later books, delves into the ruling dynamics between the various seasonal courts, though that gets blended with other plot elements. The purest 'society' exploration I've found might be in some of the older folklore-inspired works, where the politics are inseparable from the nature of the fae themselves.