You are right, it is not part of the Linux kernel. The kernel is simply not responsible for jobs like that. What is depends on your system. On the console it could be your tty driver, in most graphical environments you are thinking of are probably based on Xorg and use the Xorg selection buffer and clipboard; but you may also be using Wayland; a direct frame buffer driver or another graphical engine and the code may be elsewhere. Even in the case of Xorg, Xorg is not responsible for binding keystrokes and other events to actions. That will come dow to your Desktop Environment or Window Manager which could be a lot of things.
There is no single place to point you to without a LOT more detail about your environment. In the mean time it sounds like you need to read up more on the overall architecture of a Linux system and what systems are in charge of what sort of operations. The eventual answer to your question will almost certainly be found spread across more that one layer and you need to know how they go together to make sense of it.