`errno` is a userland concept; the kernel returns negative error numbers that libc then turns into -1 and sets errno. Thus the correct manpage is errno(3).
As a long time emacs user, I appreciated the inclusion of EMACS as an error code. When I moved from TECO to gnu emacs in to 80s, elisp was an advance. Now I have a perpetual todo item... "rewrite emacs in fennel or janet or even minimalisp."
https://man.freebsd.org/cgi/man.cgi?query=errno&apropos=0&se...
Also, your statements about the kernel and libc are OS specific.
"What was deluxe is now debris..."
If only AI threw an error when it hallucinates.
Let's hope that reference is not too obscure...