I have one idea that I'm saving for a book, but I can give you the seed of it easily enough.
Plant people. Not exactly dryads, but beings that are sentient plants with some control over their growth. The interesting parts of them as a race come as you start answering questions about them. Like, what do they do with their dead?
In my DnD setting I've taken a few classics and respun them.
My Yuan-Ti were adopted by a dying snake god and drank of his blood to gain power to fight their enemies. They are not evil, though they do enjoy empire building like most civilizations. The big thing is that they practice forms of ritual cannibalism in an attempt to reconstitute the god that saved them. The Thin-Bloods (Pure Bloods in the monster manual which is the dumbest name for the lowest caste of a system based on how snake like you are) eat snakes, especially on holy days. Then the Half-Bloods, who have the lower half of snakes or sometimes snake heads (I'm not into the snakes for arms thing. It's decent for a monster but raises too many questions about how they would live in society based around thumbs.) occasionally ask a particularly valiant or notable Thin Blood to be sacrificed and eaten by them. With the "Pure Bloods" (Called Abominations in the book, because of course the most perfect example of divinity gets called that in the culture they come from [sarcasm]) doing the same with the Half-Bloods. Now, here's the deal. This practice is sacred, and eating an unwilling person is a heinous crime. So, people can say "No, I don't want to die today", but it is also a high honor, because being devoured means your power and the collected divinity of snake blood in you (which if you are super awesome most be really high for your caste) gets taken to the next caste, and your power and Animus may be reborn in the next caste, getting higher and higher up the ranks. Not being eaten means your divine snake blood is wasted, to be reborn as normal snakes and have to work back up the ranks again. This means eating the dead is rather common. There is an immortal emperor of the Yuan-Ti who sits at the top, who is meant to eventually become the avatar for the Snake God.
As an aside, I've found that to avoid the "Humans with funny hats" problem, you need to think about the culture of the people you are working with. They aren't human, so we can't assume they would think or react like humans. A Yuan-Ti adventurer from the culture I have laid out would be horrified at the thought of their body being left in some far foreign land, they might even keep a stash of money that is specifically for paying to have their body preserved and transported back home if they die. Because that is a big deal in their culture.
I did something with the Genasi as well. Literally the children of Genies, do to an epic based off a massive war and a peasant woman being a perfect servant to the Four Great Leaders, the Genasi actually fill in a purpose as slaves and servants to the Genies. But, leaning heavily into the idea of English Buttling and taking people as possessions into people as expensive possessions. Genies like showing off, and owning the swordsman who slew seven dragons and reclaimed the sword of four winds from the Pits of Hell is like a current rich dude owning a gold plated ferrari. He's going to show them off to impress his peers. But, like that gold plated ferrari, he's also going to take care of that mortal, because how he takes care of his stuff reflects on him as a person.
And, this has effected the society of Genasi. They can leave a bad master, and the social hit of a well-respected Genasi leaving the household of a Genie or even asking to leave would be fairly devastating, but they also see their worth in literally how much they are worth. They seek out the arts and mastering tasks, because mastering something raises their value if they are sold off, and that means they are a better person. They actually have invented magical books that they carry with them, ones that copy everything into a twin book in a Great Registry. It is a log of their actions, their achievements, their embarrassments, their lineage (hey stud breeding is a thing, though I haven't considered it too much in the context of this setting yet) and their sale history.
I've got places to go, so I'll wrap up their, but more than thinking "What weird thing can I make this race look like" I'd say look for something and dial it to eleven. I know of myths where Ghouls are sentient and have their own underground empires, or you could have a race that are living elementals of magical energy, but if you never think about what that means for how they act then they are just going to be humans with strange abilities that people are likely to forget they have.