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:

1. Villainess, or other main character, learns of her future misfortune. Tries to avoid it.
2. Villainess falls to ruin (misfortune). Story focuses on her life afterwards.
3. Villainess, or other main character, learns of the state of the world. Villainess betters as a person.

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).

• I developed a strange obsession for this sub-genre through a series of unfortunate circumstances.
  • I was reading a villainess manga, then I finished all the (at the time) available chapters. So I decided to start another one, because I still felt like reading something similar. Then I finished reading all the available chapters again, but only after I got hooked on the series. Now I had an even greater urge to read something similar. This repeated so much that I’ve gone through about 50 of them and they’ve all started to blend together in my mind.
    • As a result, I’ve also grown familiar with the Aristocratic genre.
• My means of distinguishing between “sub-genre” and “genre” is almost entirely arbitrary. Genres have a much clearer picture of what you get, while sub-genres are more variable. I think.
• I believe the first of these was Otome Gēmu no Hametsu Furagu Shika Nai Akuyaku Reijō ni Tensei Shite Shimatta… (My Next Life as a Villainess: All Routes Lead to Doom!), or at least popularized the genre. I haven’t really researched it so I don’t know.