There are some fountains like this in Airports and where the tapwater is pretty bad, but usually a public water fountain is an old fountain from the medieval times with some ornaments and stuff
This is the one from my home city
But they are only outside because on the inside you just fill your bottle in the bathroom
Not all, but a lot of them. If you encounter a fountain that looks like you can drink from it and it DOESN’T have a sign telling you it’s non-drinkable, you can safely drink from it