The real enforcement angle depends on where you are in Italy and what exactly you're doing. Some cities have been more aggressive about it than others, but what actually matters is context - if you're crossing at a red light while texting, yeah, you're at way higher risk of getting stopped. If you're on a quiet side street checking a message, most cops aren't going to bother. The fines can be meaningful though, so it's not like getting caught jaywalking in some places where they just warn you.
What I'd say is don't overthink it if you're just visiting. The bigger takeaway is the safety part that other folks mentioned - seriously, pay attention when crossing. I've seen some close calls with people completely absorbed in their phones, and it's genuinely dangerous. If you're traveling there, just treat it like common sense: put the phone away at intersections, look at traffic, and you won't have any problems. The law's more about discouraging people who are actively being reckless than creating some surveillance state for pedestrians.