Most of the time I hear S N E S (each letter pronounced individually) or Super Nintendo.

I have heard “the Snes” (pronounced with an S sound instead of a Z), but I didn’t hear that commonly until much later, after it was considered a retro console.

I live in the US and me and all my friends pronounce SNES as SNess. (And NES as Ness) for what it is worth. It seems to be somewhat common as my friends who grew up on the other side of the country say it this way too.