Sanchin is among the oldest of known kata, and of course, stems from China where is was known as sa'am chien. Higashionna Kanryo learned it (possibly from Ryu ru ko, with whom he studied) in southern China and brought it back to Okinawa. This was passed down to Miyagi Chojun (Goju founder). Both these masters made changes to the kata, as did those who followed.
TSD has mixed roots including native Korean fighting, northern Chinese influence (TSD Master Kee studied there) and Funakoshi's Shotokan. From my limited Korean MA knowledge, their native fighting techniques had no kata (just as early Okinawan indigenous techniques did not.) Whether northern Chinese kung fu had a Sanchin-like kata, I have not seen such reference. That leaves Funakoshi Gichin's Shotokan as a source. His style stems from Shuri-te, as compared to Higashionna's Naha-te which was more power oriented. So, historically, Shotokan did not have Sanchin in its curriculum. At least it is not listed in Funakoshi's "Karate-do Master Text."
Since many of Korean MA katas were adapted from Shotokan, they do not have Sanchin. In more recent times, Korean styles have created or perhaps borrowed other katas. Of course, nothing to stop some Korean dojangs (or anybody else) from adding anything they want, so it is possible someone stuck Sanchin into their Dojang's course of study during the last few years.
If any TSD or TKD guys out there do Sanchin, let us know its lineage from your dojang.