Kebbi State

Exactly.

And from there, it supposedly spread westward and northward, eventually encompassing Katsina, Zazzau, Gobir, Zamfara, and Kebbi.

So an eastward origin spreading west.

Yeah.

Literally, speakers of the Hausa language.

Got it.

And sometimes the term Hausa was even more geographically specific, referring mainly to the kingdoms of Zamfara, Kebbi, and Gobir.

Basically, the Hausa lands closest to the Songhai Empire.