I think there are two ways of looking at your question, and I feel like I have read discussion on this topic before, but sadly I can't find the references again right now. If your question is primarily technological, then I agree with all the other answers here – given all other variables being held essentially the same, death by drone vs. death by mustard gas vs. death by catapult are probably essentially equivalent. As others have mentioned, post traumatic stress is a response to trauma, which can be caused by essentially any event involving extreme stress – so you should find "PTSD" resulting from medieval combat.
The alternative perspective, which again I was unable to find academic discussion about, is to look at whether a different society would experience post traumatic stress in the same way. Since we don't have experimental evidence on hand, we can only do thought experiments here, but would the experience of mass death in warfare (regardless of the weapons involved) be different for people with a radically different psychological makeup? It's often said that in earlier eras "life was cheaper" – average lifespans were much shorter and random death was much more common: through unchecked violent crime, rape and pillage raids, constant epidemics, starvation, industrial accidents, animal attacks, and so on. In such an environment, is there any sense in which the terror of combat would be less terrifying comparable to the baseline level of terror experienced in daily life? You could argue that in such a case everyone would be traumatised, but that would mean that veterans (and their PTSD) might not "stand out" enough to be recognised as experiencing a specific category of psychological harm? So that's our hypothesis one: a society could exist where the PTSD experienced by combatants was not noticeable/remarkable in the context of broader society.
For hypothesis two, consider a hypothetical society with a "martial culture". Many of the problems we face in integrating veterans into modern society involve issues specific to re-integration into civilian life: e.g. how to teach a person not to be in a constant state of readiness (which in civilian society is not normal), or how to teach a person not to respond to potential threats with violence, or how to teach a person new skills that will get them a civilian career. Here on worldbuilding we could posit a society where the is no reintegration into civilian life – a warrior culture, to lean on a cliche. In such a situation, an individual might still be traumatised by our definition, but they remain in the military context where the symptoms of this trauma may be normal, and less likely to interfere with their ability to lead a meaningful life. This kind of society could view the psychological changes wrought by combat experience to be a natural progression in an individual's life – the example of this attitude that comes immediately to mind is in Kubrick's Full Metal Jacket:
"The thousand-yard stare. A Marine gets it after he's been in the shit for too long. It's like you've really seen...beyond. I got it. All field Marines got it. You'll have it, too."
Psychology is both a taxonomy of individual experiences and a system for comparing experiences to a baseline. We observe a set of behaviours which differ from the observed norm, and we infer that these behaviours are brought on by stressful experiences, and so the concept of PTSD is created. But (and keeping in mind the distinction between psychology and neuroscience) we are talking about a discipline which deals in fairly subjective data, and tends to arrive at conclusions which are predicated upon a set of unexamined assumptions received from broader culture. So, in an attempt to work all of that into a "hard science" answer to your question, I agree that evidence shows that to experience terrifying events causes a certain set of observable consequences for those involved. In that sense, you should expect PTSD as we define it to appear in any society which is likely (in the context of their culture/psychology) to have the same basic worldview as ours. However, I see no "hard science" reason why ours is the only possible worldview, so you could maybe tell a psychologically interesting story about the kind of society that does not have a concept of PTSD.