We just spent a month in Treviso, and I was honestly surprised and the number of "squatty potties"/hole-in-the-floor toilets we encountered. Several in very busy bars and actual restaurants. Unfortunately, you don't know until you visit. Not ideal, but thankfully I'm young and able to deal with it and my toddler is male, and thought it was a fun adventure! I have not encountered any in major "tourist" cities (Milan, Florence, Venice, Rome, etc.).
One other tip that I haven't seen mentioned yet - if you search on Google maps for "bagno pubblico", you can see the locations of public toilets. I always "save" these (click on the location, look for the "save" button - the icon kind of looks like a bookmark) so I can easily find them for future reference. Once a location is "saved" in Google maps, if you download the map on your phone, you can access it even while offline.
I'll echo the recommendation to always have tissues, hand sanitizer, and coins readily available.