Fermat's principle is an outcome of constructive interference of waves. It works both for classical and quantummechanical descriptions. E.g. check https://phys.libretexts.org/Bookshelves/University_Physics/U...
True, so the interference is the "computation"(heavy emphasis on quotes) which gives rise to the principle.
> a ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in
A ray of light doesn't know or choose because it has no agency, just like an apple doesn't know or decide to fall because of gravity. It's an anthropomorphization.