Most Italian women I know would have a panic attack if they went out with a tracksuit or a pajama like Americans do. That's stuff that only happens in nightmares and if you're 20 in a slum outside of Milan. Anyway Rome is not considered particularly fashionable in Italy. You find the highest attention for this stuff in most cities in the North, with Milan being the center of the fashion industry and smaller towns being more bougie, and then in the South with the "show off the bling bling" culture more common throughout the Mediterranean. In the North, the minimum is to dress like for a fashion show, in the South the minimum is to dress like for a wedding. In the center they care less.