Kosovo is not universally recognised though, to be fair. But yes, I'd include it. Even if you are against in principle, it's de facto a state and treated as such even by many countries not recognising it in name.
But that would mean that your API should return a country specific result to be accurate.
Which is precisely what for example Mapbox does - they allow consumers to specify a worldview, which adjusts borders and other geographic features based on the specified culture: https://docs.mapbox.com/help/glossary/worldview/
They dont have Serbian one to resolve this issue. Or even more relevant ones like Russia (remember Crimea).