In Mystery of Metru Nui we can read that Kapura walked in Ta-Metru and saw Kolhii staff. However, BS01 says that Kolhii stick was first made on Mata Nui after the Bohrok Invasion. How it can be explained?
It was just a stand-in for Akilini.
Originally, Akilini was planned to be a form of Kolhii and to use the same name, but the story team later changed it to be a different sport. By the time this took effect, however, Mystery of Metru Nui had already been written, and as such it referenced Kolhii multiple times in the book.
Akilini likely was meant to use staffs at some point.