App Platform works a bit differently than droplet. It runs each component of your application as a separate, ephemeral container on the platform. When a container is unhealthy or updated, we launch a new instance and destroy the old. To that end, we don’t recommend installing tooling on running containers. You could also use a Dockerfile to build an image which combines mysqldump and your application, though we generally would recommend running this type of maintenance in a separate container.
Scheduled job containers are on our roadmap, and would be the right type of component for running periodic, scheduled backups. For this, we’d recommend using a Dockerfile to build an image which includes your back up script and mysqldump. The mysql docker image could be a good base (FROM) image for this specialized short-lived container.
Until we release schedule jobs, we’d recommend doing manual backups locally or from a droplet.