Is it possible to find a database backup within phpMyadmin or are backup files always stored locally on a pc?
phpMyAdmin does not create backups for you – unless you set up some backups yourself, there are no backups stored within phpMyAdmin nor on your local drive.
If you wanted backups, you would have (had) to either backup the MySQL storage files themselves, or create scheduled SQL exports from your databases.
Windows' or your Linux distribution's built-in backup methods would automatically backup those MySQL data files if you included their location. AutoMySQLBackup is a script for Linux that creates SQL exports on a regular basis.