How should paths in /etc/paths.d get added to $PATH?

None of the paths I have in the /etc/paths.d directory are being added to $PATH in any of the shells on my High Sierra system. Presumably there’s supposed to be something in some file that says to look in /etc/paths.d when a shell starts; what is that something and where should it be?

Ideally I’d like to know a proper way (i.e. not some weird hack that technically solves the problem but will cause more problems down the line, because that’s almost certainly how I got into this mess) to get $PATH to use the contents of /etc/paths.d for at least bash and zsh.

/usr/libexec/path_helper is used to build PATH from the default in /etc/paths and the entries in /etc/paths.d (see man path_helper for details). By default this is called in /etc/profile which is executed for each sh/bash/zsh style login shell.

On my system /etc/profile looks like this

# System-wide .profile for sh(1) and friends

if [ -x /usr/libexec/path_helper ]; then
    eval `/usr/libexec/path_helper -s`
fi

if [ "${BASH-no}" != "no" ]; then
    [ -r /etc/bashrc ] && . /etc/bashrc
fi