The spelling is intentional. Café comes from the French. It means a coffee house, a small restaurant, a place to sit. That is not wrong. But caffè is Italian — and in Italian, caffè means the coffee itself, specifically the espresso, and the bar where it is served standing up. The distinction matters. A café is a room. A caffè is a ritual.
In Italy, caffè is ordered at the bar, not at a table. It arrives in a small ceramic cup, already sweetened if you want it, and it is gone in two sips. The barista knows the machine the way a pilot knows the aircraft. The shot pulls in 25 seconds or it does not pull at all. There is no oat milk modification. There is no seasonal menu. There is caffè, and there is the understanding of what caffè is for.
The word itself traces to the Arabic qahwa through the Ottoman Turkish kahve, into the Italian caffè, and then into the French café — which the English borrowed and softened into cafe. Every language kept something. The Italians kept the sharpest version.