But that still doesn’t change anything about Mutsumi.
Even with Mutsumi at the center of the story, told from her perspective, nothing about her would change. If we say she used to be bullied, there’s nothing new to it. It’s obvious that she’s a victim-type. The way the reader perceives her would remain unchanged (Pitying Mutsumi is already a thing).
So this backstory has little use unless it introduces some changes to her character, directly or indirectly.
For example, what Pepe said, if Mutsumi’s current personality is the result of bullying. Or maybe if she has now decided to not make new friends because she’s afraid they would get targeted by whoever feels like bullying her. Or if Mutsumi is unable to make new friends because their shared experiences made Takamiya and Katsusawa distrustful and rotten to the point where they always start bullying anyone who comes near her (an issue which would need to be resolved during her route. It’s admittedly very indirect, though).