Don't worry, this one is tamer and less anger.
And spoilers ahead for Arcane
Some people say Jinx/Powder have a sort of DID or Bipolar Disorder thing.
Not scratching any of that, but I personally think it's more of her clinging to her past, which we still see she does. Some people can't let go of their younger selves, can't let go to make way for their older selves.
This can also be apparent when she names one of her guns Pow-Pow, and keeps the name for that gun up into adulthood in LoL
For example:
A 27 year old knows they have to toughen up and act like an adult, but they can't help but cling onto acting as they were when they were 15. It would feel like a betrayal, feels like an addiction.
For Jinx, she can't let go of her younger self. Not until the end, where she lets go of Powder after Powder kills Silco.
After everything she's been through, what others have put her through, she throws the little girl away because it was the insecurities of that little girl that lead her to that moment, to shooting someone she loved. She didn't need the good memories to weigh her down, just the bad to push her, fuel her rage, remind her as to why she's Jinx the fighter, and not Powder the weak.
Why she went to beat Vi's record with the fighting machine, why she tried copying Vi's exact moves in the Enemy video. Powder needed to prove to herself she was strong, as strong or more so than Vi. But when that fails with the machine and she doesn't get as high as score now as Vi did in the past, she just results in shooting it.
Jinx is the strong, Powder is the weak.
To move on after killing Silco during a panic attack Powder has, Jinx has to kill the weak link. She has to to move on.
But this all leads back to her not having DID (though she still has some disorder, has had since she was young), but her just clinging on to that last bit of childhood, the last of her good memories before the deaths of Vander, Mylo, and Claggor.