Simple. Understand that a "society" is more than just 4 game mechanics.
I mean you are able to create many distinct Human societies even though they all use the same game mechanics, right? So take that knowledge and apply it to the Khoravar, even if one of your players uses the game mechanics of a Human or an Elf.
Or if that is all too much to ask... just use the Half-Elf rules from the 2014 Player's Handbook. No one is going to get mad at you for whatever you choose to do.
Very good point about society. Historically, D&D and other fantasy games have used "Race" as the common dividing factor for fantasy societies. Dwarves guard their montains and don't trust outsiders. Elves protect forests and don't trust outsiders. Gnomes hide all kinds of places and don't trust outsiders. In my home campaign's earlier history, I took inspiration from Eberron's Khoravar to make half-elves into a species that breeds true, to justify a half-elf-specific society based on their being a common race, like so many other races were portrayed.
But these days I'm thinking that distinct racial societies may not be the best way to portray the different species. I'm kinda tired of the hateful, isolating racial tropes that fantasy has embraced in the past. It's so boringly Tolkeinesque. I've been getting over that.
Going forward in my home campaign, the only "societies" that will care about racial purity will be the ones that are not "good", rather side on the neutral to evil spectrum. And they won't be monolithic. While there is a realm of chromatic dragonborn that as a society worship Tiamat (and are therefore pawns of that evil force), there are other chromatic dragonborn that were never part of that society, and not all dragonborn are treated as being from that society. Every humanoid "race" has good and evil based on their background society and personal values, as opposed being purely racial. I love the modern D&D stories that showcase incredible biodiversity (like D&D:Honor Among Thieves, and Journeys through the Radiant Citadel). It opens up way more character options if kobolds and aarakocra ("Jarnathon!") live alongside the more common races.
Sure, a forest realm society might have a lot of wood elves, but it will also have people who just like that lifestyle, no matter their species.
In response to your comment about humans having the "same game mechanics," I'll go one step further. There have been more than one type of "human" in the game for a while now (2014 baseline human, 2014 variant human, a number of dragonmarked humans, and new OA humans for 2024). They are all still humans, despite the rules package chosen to represent them. The same could be used for half-humans if you want more variety. That said, even after 2024, everyone who has a PH14, or a DDB account will still be able to use the "half-human" rules even if they are not printed in the PH24. They aren't going anywhere.