["Wachiki" is a feminine pronoun used by courtesans/geisha to address themselves in Japan during the Edo era.

Wachiki usually begs for forgiveness even when they haven't done anything wrong.]

Based off a phrase commonly uttered by a Kogasa yukkuri.

It's actually based on canon. Though Kogasa mainly refers to herself as the standard "watashi", in Sanae B after Sanae suggests Kogasa is behind on things, Kogasa catches the implication saying "What, you mean I'm behind the times?" while using "わちき"/wachiki for I.
なんと、わちきが時代遅れともうすか