Humans are the "default race," and all the other races are defined by how they vary from humans. Sometimes this is physical (pointy ears, wings, etc).
Often though, other "races" vary from humans culturally. Dwarves are traditional, halflings are plucky, orcs are savage.
I think you will find all races in D&D vary from humans physically, because otherwise they would just be human. Race in D&D is used much more like species in reality. So it has little to do with the American idea of race.
Most races also differ culturally from humans, these are often presented as mono-cultures*, although some races have subraces, like Dwarves and Elves, and these again have separate cultures and often separate physical attributes.
*They are normally only presented as mono-cultures in the PHB, when you see all the different rich and detailed settings of D&D it becomes clear that not all Dwarves and Elves are the same. But you only have so many pages in the PHB and you need to establish a base line so you can show how other groups move away from that.
And if you are half of one of those races? You still carry those stereotypes. You are defined as a half-orc, a half-elf.
This, then, is what I find very American about race in D&D. It's used as an othering tool. It's used to conflate physical differences and cultural differences. And it's used to define how player characters get to treat others. And it's tied inexorably to skin color!
Except it isn't dark skinned humans aren't evil in D&D, Wood elves and gnomes according the the PHB have dark skin both considered Good aligned, as are Dragonborn regardless of their chromatic (inc. Black) or metallic origin.
You can kill a drow because they are evil. How do you know they are evil? They are cursed with black skin!
Well and the fact their culture and society is bound to worship Lolth the Spider Queen, an evil deity.
Do you even know why they are dark skinned? Because they are based on Norse mythology of the
Dökkálfar, dark skinned elves that live underground. The myths and folklore that D&D is based on are all considerably older than Lord of the Rings, and older still than the slave trade (well the African slave trade anyway, the Norse took slaves from the European people they raided (lots of people did back then)). Dwarves and gnomes and loads of stuff can be traced back to European folklore before Europe had even started empire building.
Dark is associated with evil, and light good because the night was bloody scary when wolves could drag people away from camp fires, it has nothing to do with skin colour. These myths and folklore were built on deep seated fears from pre-history.
Of course, this is not universal. But it is systemic. The very existence of Drizzt shows that in order for a Drow to be anything but evil, they have to turn against their whole society.
Again because that society worships a Chaotic Evil deity.
To me, race in D&D is very Americanized because it echoes so many ways race was used to enslave, kill, discriminate against, and segregate people based only on their ancestry or skin color. Race in D&D is Americanized because it conflates "dark" with "evil." And Race in D&D is Americanized because it's obsessed with bloodlines and ancestry.
And yet oddly it isn't these dark skinned races that are kept as slaves, almost always in the D&D it is the evil races that are keeping slaves, and you know why, because keeping slaves is evil, D&D teaches slavery is evil, doesn't sound like support of racist ideas to me.