Got the Fiat 500 out for a spin with its new battery. Started first time! ⚡ And I think I've discovered why it feels more powerful than our old one. It's a late model Giardiniera, and I found this article about the engines:
https://www.fiatvanderlaan.com/kb-docs/fiat-500-autobianchi-giardiniera-engines/

I checked our engine number and it is a "4000000 engine", one of the last ones, so it is bored out and capable of being a 597cc block. I bet the guy that sold it to us has put 500R cylinders in it, that would make it 20% more powerful than standard!