It’s not really a twist though, the only real twist is that the mother isn’t actually crazy. It’s kinda been hinting at and showing that something is wrong with her. I think it does it pretty well too, the protagonist even hints at something feeling off the entire time. I wouldn’t say she’s murderous exactly either, the fish is the perfect analogy for it.
She could put the fish back in the water and save it’s life, but instead she chooses to monopolize what it needs. She controls how much water it receives, prolonging it’s life and struggle, but allowing it to keep suffering. Ultimately, allowing it to die on it’s own. Then she crushed it.
Interestingly she didn’t show joy at the boy dying. Maybe we will get more context eventually, since the mother’s recollection was distorted in its own way. Since we don’t know how active her role in his death really was, we were left with more of an implication and no clue on severity.
Though we have the most recent incident as well to look at for further detail. She controlled the relationship the MC had with her friend, managed to insert herself as a mediator. This allowed her to control that lifeline to an extent, and influence it. Though she didn’t control it too much. It’s more like she deprived it, and observed. She didn’t step in to help at certain points, or resolve certain issues. She let it play out and watched. Then, she nudged the girl in a certain direction. She didn’t force her or coerce her.
It’s actually a kind of terrifying character. She doesn’t play an active role, she just offers just enough help. Nothing more, and then pushes them off at the end.
We can actually observe this behavior towards the MC already as well. She probably gets it from her father. During the Tiger cub discussion we see exactly the same trend, she sees a potential avenue for downfall and doesn’t warn MC about it. The mother does. She wants to see the MC succeed, only to be shackled, and inevitably taken care of like the man her father described. She sees it happening, but doesn’t step in at all to stop it, or encourage it.
I think she’s the type to make some one completely helpless and dependent on her, until all they have is her. But she never gives them enough help. She never tries to solve the problem, or fix anything. Enough help to be salvation, but not enough to escape. Only to struggle. Then, eventually, when her help isn’t enough, when you can’t struggle any longer, she takes pleasure in it. She takes pleasure in peoples own personal downfalls. Not in killing them.

https://m.comic.naver.com/webtoon/list?titleId=837455
The story really grips me, but I’m not a fan of the plot twist where the potential close friend (rich silver-haired girl) turns out to be a murderous, obsessed psychopath.
I've already seen this trope in other Asian and Western soap operas, melodramas or thrillers.
Examples:
Single White Female, Dreaming Freedom, High School Queen etc.
I get that every hero needs a villain (Barman vs Joker or Superman vs Lex Luther), but I feel that society and the system ruled by patriarchal, conservative elites are already enough of an antagonist for our underdog protagonist.