I haven't lived in Italy for 10+ years, so I don't know if anything has changed since, but that was the limit for all houses I've lived in, and from a quick Google search, it depends on your contract — the lowest is a 2 kW limit, 3.3 kW is the most common, and you can ask for an increase for an additional monthly fee. Heating and stoves are usually gas-powered, we don't do electric except for water boilers.

I have always wondered if those limits and the high electricity costs are because Italy abolished nuclear energy post-Chernobyl, doesn't have a massive oil and gas operation, so most of it is imported at a premium.