I'm gonna ruin it by saying that this is portraying her last day, Akyuu knows that her time has come so she wants her final moments to be with a close friend sharing a nice and comfortable moment, maybe she requested Akyuu to read her something like a fairytale so she can drift away to the sound of her voice, and Kosuzu is oblivious about it, thinking that Akyuu is just more chummy than usual.