Why S_ISVTX from /usr/src/linux-headers-X.X.X-X/include/uapi/linux/stat.h is called S_ISVTX? What stands for the letters in the name?
Quite right. It's from old days, where the TEXT-segment of executables in that special directory would not get freed at once, but kept as long as memory resources permitted it. Applications would start faster. This behavior is obsolete by now, never used in linux as far as I know, and now it is used for access modifications. (See IEEE Std 1003.1-2017, 4.3)
So it is "SaVe TeXt-segments".