Do either of you know if this “Way of Horus” is AKA either “the Way of the Philistines” or the “Way of Shur” on Biblical maps?
no, I do not, sorry.
The Way of Horus was the path used by pharaonic armies moving to and from Canaan, Philistia, Israel, etc, as well as points east. Generally the Way of Horus is attributed to 18th dynasty (New Kingdom) pharaohs and those subsequent, but it may have been around long before that. It is described (in its then-current form) by Herodotus.
The Way of Shur led to the Hyksos capital of Avaris. The Way of the Philistines I’m not sure about, may have been the same route/road.