Before we can derive the meaning behind the word, we need to first understand where the term originates. These sages can be considered philosophers that use their wisdom to help shape the foundation of Chinese culture, society, and even politics. But is that all?
Because much of Eastern Asian culture, language, and philosophy were borrowed from the Chinese to some extent, (I understand there are exceptions), for brevity I will focus mostly on its Chinese origin.
There is a work originating from before the Xia Dynasty concerning the "Three Sovereigns and Five Emperors" (三皇五帝, Sānhuáng wǔdì) (who they are differ depending on the source [see link]. I will not attempt to name them in order to avoid confusion). In it, there are three figures regarded as "Three Sovereigns," who are hailed as "god kings," and are considered the ultimate cultural heroes (and regarded as demi-gods in the myths) of Chinese history. They are said to have had magical powers and are credited with the basic technological inventions, social structure, and political norms of the time. During despotic times these figures are said to have been invoked as paragons of leadership.
The "Five Emperors" subsequently were regarded as legendary figures,"sages kings" depicted with perfect moral character. These figure were more worldly but historically intangible figures, like a mythical tribe leader, compared to the "Three Sovereigns," who were considered divine beings.
In essence these can be considered the first "sages" of Chinese legend.
Confucius is known to have revered these figures, Emperor Yao and Emperor Shun (two of the Five Emperors, according to some sources), Yu the Great (described to be a decendant of the Yellow Emperor, one of the Three Soverigns by some sources) the three true sages 聖(人) (Shèng[rén]), as the pinnacle of human perfection, the equivalent of a saint in some regards.
In Taoism the equivalent would be "仙" (Xiān), (the character itself can mean hermit or rather literally "mountain person"［人＋山］), related to Eight Immortal Scholars of the Han, but the meaning has changed quite a bit over time. Thus the meaning of those two titles by themselves are the equivalent of the Buddhist term for the "enlightened/awakened one" (Buddha, which is a title, not a name).
In short, the title of "sage" is what you would call an "enlightened one," in a philosophical and/or spiritual sense. While the names may differ their end destinations are the same. Both Confucianism and Taoism walk the same path, but their ideals about it are different. Taoism seeks to free itself from worldly desires (as a hermit would live, confronting problems through the way of nature), but Confucianism is more about being a man of action, upholding the established hierarchy and fulfilling their given role as best they can (i.e. conquering problems through cultivating intellect and morals).
"They are generally people who have 'transcended' humanity, possessing supernatural powers, and very long lifespans"? This question would be much better if it was about a specific story or portrayal of a "sage".