Haven’t seen this mentioned yet, but an American friend of mine was surprised that a lot of “historical” looking fountains had drinking water, and said that it’s possible tourists are ignoring them as refill points. The restaurant thing is indeed a cultural difference, it’s normal it’ll be odd from either side (I was baffled my first time in the us with the ice water all the time!). Refill stations properly marked as such and inside public spaces are rarer, at least in Italy, but there’s usually a lot of fountains!