It has nothing to do with looking like Milano
They call it the Milan of the south, because it is the financial centre of the south(Milan in the financial centre of the country), and the fashion capital of the south(Milan is the fashion capital of the country), etc. Infact many people buy their clothing in Bari, because you get all the designer clothing you get in Milan for a fraction of the price.
Bari is in the process of restoring their entire downtown district.
One of the projects is restoring Corso Cavour. This is what it will look like.