Looking at the examples provided, this appears to be very similar to the so-called "ergative" usage pattern in English, where a semantically transitive verb (a verb that conceptually requires an object to make sense, even if that verb is not stated in the sentence -- things like "eat" or "read") is used intransitively, and where the subject of the now-intransitive verb is usually the object of that same verb when used transitively.
In the oldest such verb pairs, the basic yodan form was intransitive (like つく or たつ), and the shifted nidan form was transitive (like the modern ichidan forms つける or たてる). This basic mechanism was then later used in similar fashion to mark the shift in valence for transitive yodan verbs and their intransitive nidan counterparts.
Regarding 出来【でき】る
There was a separate question a couple years ago about the derivation of the word 出来【でき】る. Please see my answer post over there for a fuller exploration of where this word came from.
In specific relation to your own question, the relevant details are:
- The word itself stretches back to the beginnings of written Japanese in the 700s.
- The sense "to be do-able" first appears in the late 1600s. This seems to be a reasonable extension of earlier meanings of "to spontaneously become manifest, to come into being on its own".
I am less certain how potential was expressed prior to the appearance of these two things, the "to be do-able" sense of verb 出来【でき】る and the 可能動詞【かのうどうし】 or "potential verb" forms of regular verbs. Clearly, I should study Classical and Old Japanese in further depth. 😄