well from a description of one of RAKRRRR other doujin following this same Paro.
they said it’s a “Geisha Mercenary” Parody. So that’s why Levi’s always holding a Shamisen. They also said that they wanted to see Levi and Eren fight enemies in that kind of setting.
I’ll be translating that part of the Parody tomorrow, so maybe that will give you a better idea.