First, clone the repo with the completion scripts:
git clone https://github.com/capezotte/s6-shell-completionAdd . "$path_to/s6-shell-completion/bash/s6-rc.bash" the end of your .bashrc.
mkdir -p ~/.local/share/zsh/functions
ln -s "$PWD/zsh/"* ~/.local/share/zsh/functions/s6-rcand restart zsh.
Tested on a stock Artix s6 configuration, and a Gentoo install with a custom s6 repository.
This scripts goes quite far to ensure it is distribution-agnostic and respects compiled-in distro defaults with as few assumptions as possible.