“Wizard” and “Magus” are both terms that could be traced to just meaning “a wise person” or “a person with knowledge”. Knowledge is power, and sufficient amount of power can be perceived as supernatural.
After all, any sufficiently advanced technology is indistinguishable from magic.
Neutral medics? That would likely be a shitshow to balance, but I would actually be interested in trying that. Lore accurate Swiss Mercy!