Now that the changes to the dirname(3) function had some time to settle,
let's go ahead and use the same approach for replacing basename(3) by a
simple implementation that modifies the input string, thereby making it
thread-safe and guaranteed to succeed.
Unlike dirname(3), this function already had a thread-safe variant
basename_r(3). This function had its own set of problems, like having an
upper bound on the pathname length. Keep this function around for
compatibility, but remove most references from the man page. Make the
man page more similar to that of dirname(3).
As the basename_r(3) function is only provided by FreeBSD (and Bionic),
depending on its use is even more implementation defined than assuming
that basename(3) is thread-safe.