A cathedral has nothing to do with size of the church. If a church has a bishop resides, it's a cathedral.
Source: not religious at all but my brother is a dominican friar so has explained this stuff to me. Also confirmed by this for example https://catholicsay.com/differences-between-a-bishop-archbis...
The word cathedral comes from a Latin word meaning “seat.” The seat referred to is the seat of the bishop, who is the leader of a group of churches related to the cathedral. The bishop's seat is both a metaphor for the cathedral as the bishop's “seat of power” and his actual chair, the "cathedra," inside the cathedral.
It's not a possible word in Latin; it would have to be a loan from Greek.