Generally it does not respond to the original question, but..Caodemarte wrote:Vajrajana was certainly well known in China. Forms of Tantric and Esoteric Buddhism , such as Mantrayana, (Shingon being the Japanese version of Chinese Esoteric Buddhism) were well known in Korea in ancient times, both directly from India and through schools that included it such as Tientai. You can also see this in old Buddhist art in Korea. I don't known how long practice survived, but it would be odd if Korean monks did not study at least some classic texts. Of course, some Korean monks went to China and at least one taught Buddhism in Tibet (check out Buswell's articles on Korean influence through the Chinese cultural sphere).
There is no any Indian vajrayana transmitted to Korea via China. There are no reports of it like hundered years ago. So as you say they were well known in ancient time, but simply did not survive. Todays esoteric school in Korea is modern development without historical relation to unbroken lineage.
As for chogye what i have seen in manuals of chogye monks was actually from Japanese shingon. In China shingon school called 真言 Zhēnyán was not existing any more during Yuan dynasty. So Mongolian emperors actually were under Tibetan sakya influence.
Chinese do not even recognize Buddhist vajrayana sculptures in there own temples like 靈隐寺 in Hangzhou, which they told me that those are some sculptures from Mongolian time and of their own religion (!).
As for chan sutras, one more thing, they were not yet popular in Tang or Sung dynasties, if they were, for sure there would be clear transmission of those texts within zen lineages to Japan. But it did not happen for over 300 years of intensive zen relation between China and Japan. They became more popular during Ming dynasty when in China zen was in decline and became more syncretic religion with strong pure land influence and other elements, which was strongly opposed before. And in fact they have hardly any connection to zen, though they may be used as some means of education.