We have been in Venice, Florence, Cinque Terre and Rome, plus quick days trips to Pisa and Pompeii, these last couple of weeks. We flew in on Air Canada. Here's our mask experience.
Air Canada enforced masks, including telling people to cover their noses and announcing food service is over and time to mask. Surgical masks were fine. They provided kits with surgical mask.
Vaporetti in Venice: they enforced masks, but not type of mask. The always checked that you had a mask with you if it wasn't already on and they will turn you away if you didn't have a mask.
People wore masks on trains and they kept running announcements about it being mandatory. All but one time, surgical mask was fine. The one time, strangely, the employee checked tickets and didn't say anything about the surgical mask and then woke us up later to tell us to change masks. This was on Trenitalia. In the train stations, it was mixed between people wearing masks and not.
Rome Metro and bus: everyone wore masks but we didn't notice any enforcement.
Rome taxi: there was a plastic barrier between front and back seats. We had one driver who didn't wear a mask and one who did. We didn't wear them in the back seat and no one said anything.
Circumvesuviana to Pompeii: only public transportation where some people didn't wear masks.
None in our group of 5 had a cloth mask and I didn't notice anyone with cloth mask so can't say how those would be treated. Also, common to see people having them on but not covering their nose, stuff like that.
St Mark's Basilica was requiring masks (surgical fine) but Doge's Palace was not. Not required at Uffizi, Accademia, climbing the Duomo in Florence, nor for climbing Tower of Pisa. Most of the things we've done in Rome are outdoors, so I don't have a good report. We bring ours everywhere and just follow what everyone else is doing. Tested negative this morning, just in time for the last day that it's required...cost 95 euro for 5 of us. Great timing for us! Oh well.