This is a sub-genre of the Aristocratic genre that focuses on the villainesses.
It also frequently overlaps with the Isekai sub-genre.
In many romance Aristocratic media, there is typically a girl, the villainess, who bullies the protagonist for getting close to the male leads andor inconveniences the protagonist in other ways. From what I understand, Otome games (dating games aimed at girls) have turned this character into a standard, easily-identifiable archetype.
This “villainess” character is what this sub-genre is built around. This character is usually the protagonist or, if not, a main character. In both cases, the plot focuses on this character.
For one reason or another, reincarnation plays a part in the plot. One of the characters, usually the villainess herself, tends to have reincarnated. Off the top of my head, I can’t think of a single villainess story I’ve read that doesn’t have reincarnation in some form. As a result, the villainess sub-genre frequently overlaps with the Isekai sub-genre.
The plot tends to go one of 3 ways:
However, stories in the villainess sub-genre can go all sorts of ways. Especially since these plots aren’t very rigid.
As reincarnation is extremely common, the character that learns of the world tends to do so because they remember it from their previous life.
The setting of this sub-genre is usually tied to the Aristocratic genre, with a lot of influence from Otome games (and web novels).