In his book, History of Madness, Michel Foucault attempts to provide a socio-historical account of how the notion of 'unreason' has shifted and become reconfigured over time in the Western European context. Foucault makes a complex and varied argument. One possible reading (and answer to your question) is that 'unreason' was, until around the 18th century, a particular form of knowledge or 'reason' that was legitimated and constituted within cultural and social contexts (e.g. mystics, seers, shamans, etc). Foucault argues that around the 18th century the notion of 'madness' began to emerge in conjunction with psychiatry and 'authoritative' or expert knowledges that subjected unreason to a sort of clinical gaze that constituted it as invalid and a sign of mental deficit in the subject, and so forth. The lines between unreason, reason, and madness became entangled with emerging forms of psychiatric and medical knowledge that focussed not on the body but on mental states, that is to say, the mind as an object of inquiry. Systems of categories and classifications emerged to provide a sort of knowledge-power infrastructure to support the development of what madness is and how we should deal with it. What we observe is that unreason becomes a subjugated form of knowledge - it becomes the purview of artists and specially sanctioned spiritual figures perhaps. Madness becomes a social problem, and one that can be dealt with through both old and emerging practices and techniques, such as cellular discipline (locking people up), interventions (psychiatric help), and medical procedures (such as lobotomies), to name a few. Foucault has nothing to say about the 21st century because, very sadly, he did not live to see it. I suspect he might be somewhat happy to see contemporary cultural forms and practices that could revalidate and revitalize 'other' types of reason, but perhaps also acknowledge the very real or 'non-constructed' biological realities of mental illness.

While there were some people in the Bible who were described as hearing voices (e.g. the young Samuel), it is more common for them to describe either visions or a physical event in the real world.

Visions can be quite simple such as Jacob's vision of angels going up and down a ladder leading to heaven - in this case vision seems synonymous with dream, but with a layer of interpretation (bear in mind that dreams were held to be meaningful at least some of the time). These probably would not trigger a psychiatric interpretation in modern times - we all know that dreams are odd, and most people ascribe a certain amount of meaning to some of their dreams, even if it is only at the level of "wish fulfilment".

Other visions are more complex and structured - this seems particularly true of apocalyptic writing. However the resulting narratives are coherent and develop themes - in great contrast to the rambling text we often see from people with psychiatric problems.

Physical events are recounted in a way which doesn't leave much ambiguity: the author does not mean them to be confused with dreams, visions, voices or anything else. An example would be the meeting of angels with Abraham's family and Lot's family, with physical consequences in the real world.

Because of the difference between what is described in most of the Biblical texts and the experience of most psychiatric patients, I think it would be unwise to assume that they describe the same mental events. You have the option of saying that the Biblical event did not happen, or the description was greatly changed from the original event, but then you have to make a lot of assumptions to get back to what you think was the "original" event which you want to compare to modern psychiatric problems.

I apologize that I can't source well because I'm at work on my phone, but let me chime in from a medical perspective.

When talking about mental illness, it's important to note that part of the definition of mental illness is cultural. That is to say that to be mentally ill, you need to be acting inappropriate to how people within your society would act. This, if you are within a society where it is "normal" (relatively speaking and perhaps not the right choice of words) to hear voices then you are not mentally ill.

In some cultures today, hearing voices is not necessarily psychosis depending on a variety of factors. I will give a hypothetical example. A Pentecostal is in the ICU visiting a family member who has a grave illness and starts speaking in tongues and then collapses - are they having a stroke or merely expressing grief in a culturally appropriate manner for them?

I can't speak for the culture of the eras you have mentioned, I merely continue the common refrain that you cannot necessarily use modern definitions of mental illness on ancient texts because there is a lot of wiggle room.