Well, I was able to fix this and have Seafile now running with podman.
# Create seafile container in seafile pod
podman create \
--pod seafile \
--name seafile-seafile \
-v /srv/share/seafile/data:/shared \
- -e DB_HOST=localhost \
+ -e DB_HOST=127.0.0.1 \
-e DB_ROOT_PASSWD='mysqlrootpw' \
-e TIME_ZONE='Europe/Zurich' \
-e SEAFILE_ADMIN_EMAIL='fujexo@c0d3.ch' \
-e SEAFILE_ADMIN_PASSWORD='sadfHH&Ad9sadf' \
-e SEAFILE_SERVER_LETSENCRYPT=false \
-e SEAFILE_SERVER_HOSTNAME='seafile.hcorp.c0d3.ch' \
docker.seadrive.org/seafileltd/seafile-pro-mc