Why does the Linux man pages have information for C functions, that are not part of the kernel's API? For instance, strsep
Sure, it's useful to provide this functionality, but from a modular perspective, it seems like this should be managed/imported from ANSI.
The Linux, Unix, and POSIX manual pages document the Linux, Unix, and POSIX systems. A system is a set of things (in these cases, many things) that work together. They do not just document the kernel part of the operating system. They document commands for users, commands for programmers, utilities for system administrators, routines in libraries for programs, system calls for making requests of the operating system, and other features of the entire system.
When the manual pages were started, there was no C standard from ANSI, ISO, or IEC, and so it would not have been possible to defer to those organizations. Further, many of the routines provided by these systems specify behaviors beyond those of the same routines in the C standard library.