The teacher isn't a scapegoat in this, she's merely a vector for the attack. It's the "bullied" girl who's the scapegoat.
The reason people are shitting on the teacher for her part in this is less because they're buying into the blame being pinned on her or anything like that, and more because it's her job as the only actual adult in the situation (and as a person of authority, at that) to handle the situation fairly and responsibly. A task at which she failed quite spectacularly by making it a public execution of sorts right off the bat instead of pulling the accused aside to get their side of the story first and then evaluating how to proceed from there.
Like, yeah, the ex is being a manipulative bitch, but that doesn't absolve the teacher of failing to be a responsible authority figure. Hell, it doesn't even absolve the "bullied" girl for her part in all this.
I mean i guess i should give up at this point.
The mangaka has obviously tried to portray the teacher of being in a rough situation out of her depth and instead of people sympathizing with her for being dragged into a false bullying situation by the antagonist, they are instead attacking her because she isnt handling the situation perfectly, which is exactly what the main villain needs for the story to progress.
The entire previous arc would not have happened if say, the main protagonist wasnt a coward and came forward about being bullied, because it would have hurt the antagonist's reputation and ruined her chances at catfishing the star athlete boy. Even he had his chances to stop being a jerk and just tell her off because he didnt want to help her attack her ex, but he didnt.
Manipulation tactics extend deeper than just attacking a single person, its a pattern of exploititive behavior where the person pulling the strings effectively forces people into falling in line with their narrative whether they are doing this knowingly or not and all this to isolate their victim.
There will always be secondary victims who result in damaged reputation from beleiving the liar, or react strongly and wrongly to false allegations.
I feel bad for the teacher but i think im done talking about this.