I didn’t mean to put forth a thesis, just point out that two of the mark types on the axe are consistent with modern metal working tools. How that relates to the creation and history of the object I don’t know, and there may be other ways to create those marks that are just as plausible
On the grinder marks, since the machine is not firmly held in alignment with the work piece, when the spinning shaft hits the metal object the torque immediately kicks it away so you have a hammering effect as hand pressure pushes the tool down and its own oscillation kicks it up every revolution.
Vice jaws are usually padded in one way or another when working soft metals, sometimes ineffectively; and workers will also make wooden shims to assist in holding irregular objects, so not seeing the other jaw of the vice imprinted on the other side of the object does not mean those are not vice marks…but I don’t know that they are, either – they just look like such marks.