I've been mulling over how to depict the fae in my own stories so how what might you suggest would be a few good ways to write them instead of making them basically just elves, like you criticized?
you sent this right before i made another post in that thread, but i'll copy-paste what i put there and add some more on/elaborate!
complete, magically enforced inability to lie. this doesn't mean they can't be deceitful! i love fae that have to be VERY careful with their choice of words; it puts a fun obstacle in place when writing them.
in that vein, inability to go back on deals or not follow through with them. if they make an agreement with someone, they have to adhere to it. this is another place where being careful with your words comes into play; some fae that do want to come out on top can promise something that sounds good, but when interpreted literally it's not very great at all for the person they're bargaining with.
strict adherence to a ruleset that does not come naturally to mortal folk, often to the point of getting the mortals they interact with in trouble with them. this can involve rules regarding hospitality, etiquette, and daily living, as well as whatever else you could come up with. perhaps the "never take food from a fae" rule isn't so much that they'll entrap you, but that accepting their hospitality means accepting something else you might not otherwise agree to. maybe you should never say "thank you" a fae, otherwise you'll owe them.
use of “glamour”. as in, the more humanoid appearance you’re seeing and interacting with isn’t what they actually look like, there’s a big monstrous beastie under there. this is one of my favorites. maybe they can look very similar to elves! ...but that's not actually what they look like. i have an OC that's like this; elven-seeming at first glance, but underneath he looks like a bipedal mixture of a stag and a barn owl. you could incorporate the idea of seeing stones with this; rocks with a hole in the center that if you peer through you can see a fae for what they really are. there is also the folklore around seeing a fae's true form when you look at them out of the corner of your eye, or the one where they never quite get their humanoid disguises right, so you can spot them if you know the tells. there's a lot of possibilities, and use of this trope makes them feel way more uncanny and alien.
embodying whatever court they’re a part of, in the sense that they are more like manifestations of the forces of nature associated with their seasons than they are people sometimes. this isn't as limiting as one might think. winter fae can be ruthless and cruel, yes, but they can also embody the feeling of togetherness winter can bring around the holidays. perhaps there's a difference between a summer fae who embodies the beginning of summer, one who embodies the dog days of summer, and one who embodies the transition into fall.
on this vein, actual attention being paid to the court system if it exists at all. if they're broken up into courts, why? are they just the seelie and unseelie courts, the seasonal courts, a combination of the two, or a different court system entirely? i'm partial to two "main" courts, seelie and unseelie, which are further broken into the seasonal courts; seelie is summer and spring, unseelie is autumn and winter. but there's a lot of ways you could do it. what do these courts mean for the identity of a given fae? what does it change about them? the issue i take w a lot of writing that uses the courts is that it doesn't use them to the fullest extent, which makes them functionally the same as human kingdoms. these aren't humans! that's why i mention them embodying their courts. they don't have to, but i think if you want to use the courts at all you should have good reason for it!
extreme! heightened! emotions! when they love someone they are MADLY in love with them! when they hate someone they are MORTAL ENEMIES! sadness becomes a deep depression, happiness becomes utter elation. it's hard for them to contain it! this has some ties to folklore and i really love it a lot; maybe the fae just don't process emotions the same way humans do. maybe they're acting completely reasonable by their standards!
not knowing or understanding the limitations mortals have. sometimes they do things out of kindness and are genuinely well-meaning but they’re so alien to mortals that they can really really hurt them with this kindness. this can be part of why the fae are seen as dangerous; even the "good" ones can and will hurt you, they just don't know they're doing it.
“fae” being an umbrella term for multiple kinds of creatures! high fae and elves and pixies and hobgoblins can all be kinds of fae! brownies are a kind of fae! there's so many things that have been called faeries over the course of history, i don't see why not take full advantage of that.
not something based strictly in folklore, but an interpretation i'm partial to: fae being the physical manifestation of the very existence of magic and/or chaos in the world. without magic, there are no fae. without fae, there is no magic. combine this with the seasonal court system, and fae become the reason why the seasons change at all. any disruption to their people could have disastrous consequences for the mortal world.
in general i recommend looking into fairy folklore and stories and seeing what interests you most, because these are just the tropes and questions that are most interesting to me! there's a lot of stuff you can do with them to differentiate them from typical depictions of elves.