Johnathan Strange and Mr. Norell was a delightful book about adults interacting with faerie (among other things). I'd say that if you really want to maintain the wonder of the fay while having a hard magic system, it's totally fine to have faeries with explicitly delineated powers, so long as you don't tell the PCs what they are (and make them different enough from any of the standard magic systems as to be not obvious to the players).

To make the faerie different from normal enemies, make their powers strange and not deal direct damage. For example, if there is something the faerie doesn't want a character to talk about, any time they open their mouth to discuss it then instead find themselves talking about the weather or what they ate for breakfast or this FASCINATING biography they just finished (no saving throw, but a clever figure might find a way to talk around it). If a faerie wants to kill someone, they don't throw a lightning bolt, they cast a version of Irresistable Dance that compels the victim to dance ecstatically until dawn (or until their heart gives out).

Definitely put limits on their power (maybe they can only compel one person at a time, or maybe they can only use their abilities on people who have given offense, maybe they are incapable of lying). But also definitely don't let the players know what those limitations are. Ideally they should work them out for themselves, either through direct encounter or researching the history of their nemesis.