I reworked the git post-hook to publish this blog. This is the code
#!/bin/bash
GIT_REPO=$HOME/blog.git
WORKING_DIRECTORY=$(mktemp -d -t ci-XXXXXXXXXX)
PUBLIC_WWW=/var/www/pacbard.duckdns.org/public/
MY_DOMAIN=https://pacbard.duckdns.org/
set -e
git clone --recursive $GIT_REPO $WORKING_DIRECTORY
/usr/bin/hugo -s $WORKING_DIRECTORY -b "${MY_DOMAIN}"
rsync -rltvzc --delete --omit-dir-times --no-o --no-g $WORKING_DIRECTORY/public/ $PUBLIC_WWW/
rm -rf $WORKING_DIRECTORY
It rebuilds this blog every time that I push to its repo. It works ok but there is probably a better solution out there.
By the way, I now host this blog on Oracle cloud always free virtual machine. It is working well so far.