You are correct that the manual section 2 is "for" system calls, but in practice today these are just the lowest level of the C library, and not the actual system calls.
My copy of the clone(2) manual page hints at this by commenting /* For the prototype of the raw system call, see NOTES */
and more explicitly in its body text by saying "The main text describes the wrapper function; the differences for the raw system call are described toward the end of this page."
Other modern stuff is the same way, the section 2 documentation is describing what an ordinary C programmer needs to know, but if you're say, implementing the C standard library or writing a compiler for a language that runs on the bare metal you need to read the kernel documentation which is not provided as manual pages.
Huh? I saw that the manpage for clone() is in section 2, which AFAIK means it's kernel API, whereas C library functions are usually in section 3. Am I mistaken?
Even syscalls(2) refers to clone(2) in its list of syscalls.