If I look up Linux system calls on Wikipedia I get diagrams showing glibc wrapping the Linux system call interface because that's what you're supposed to be using. If I look at Linux man pages what I really get is glibc man pages with the actual system calls being almost an afterthought. Glibc wrappers actually do a ton of stuff like add cancellation mechanisms. Glibc also drops support for system calls that break their threading model such as clone.
It's the same problem with systemd. I look up Linux init system man pages and get systemd stuff instead. I expected to see kernel APIs useful for writing my own.
The library and kernel interface are more separated in Linux systems than in prior Unixes, with user space C libs being totally separate projects.
Over a Linux kernel you can find glibc, ucLibc, musl, Android s Bionic (newlib derivative from BSD), ...
It can be implemented as a small function, that first appeared in 4 BSD. It's available in Linux.
$ man syscall
(Unfortunately, this function, lives in glibc. Obviously, though, it doesn't have to. All I'm saying is that this, or a similar function, can be a linkable symbol in some small compiled object file, and not an inline primitive that has to live in the compiler.)