You got me curious and I went to check the raws. The original for "perish the thought" is そんなことないよ...!
Which isn't formal at all. Literally, word for word, it means "such a thing doesn't exist" and is just a casual way to deny something that was said.
In context, it probably should have been translated as "Of course I have!"
The translator is probably a beginner.
god, that's just plain old between-friends speech! there's no formality whatsoever.
and as for the "there's no standard teen girl talk" thing, sure, there isn't. but contextually soprano is a popular teen model and can act the part, it's not like she's a withdrawn bookworm in present time. "shabby" is really outdated however you look at it. the only explanation would be if the TLer is british, because maybe they still use it there? idk? but otherwise it's a poor choice of phrasing.
i apologize if my tone came off hostile. i guess it hit a nerve somewhere, but i don't mean any ill will toward the TLer. just uh, maybe get someone more experienced to QC?