Are we considering eye ray tracing "forwards ray tracing" or is it "backwards ray tracing" since it is the opposite direction that light is traveling from?

This should be the standard forward ray tracing where we trace ray from our eye point to potential light sources, I don't think there is any backwards ray tracing options, since we only care about the shadow of the a point or a pixel from all light sources in the environment. The number of rays to perform equals the number of pixels we want on the image in front of our eye (or behind if we are considering the pinhole imaging.

This page refers to eye tracing as backwards ray tracing, but in general it recommends referring to backward or forward ray tracing as eye tracing or light tracing because it can be confusing based on convention. https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-ray-tracing/raytracing-algorithm-in-a-nutshell.html