Hello Andre,
Kicsktart is only extracting the JPA, JPS or ZIP backup archive. It does not restore your site. The actual restoration script is called ANGIE and it is included in the backup archive at the time of the backup.
Akeeba Solo is able to backup and restore any script or application written in PHP and using a MySQL / MariaDB / Percona database. However, Akeeba Solo currently doesn't have an ANGIE installer specifically written for OpenCart. We have so far only written installers for Joomla!, WordPress, PrestaShop, phpBB3, Magento, Moodle and a generic installer for other applications. Since there is no installer specific for OpenCart you'll get to use the generic installer which simply restores the database content but performs no reconfiguration of the application. This allows you to restore your OpenCart site anywhere. If you are restoring on the same server and location no further action is required. However, if you are restoring to a new server or location you'll have to do any necessary application reconfiguration manually. I believe this only involves editing the config.php file of OpenCart, but I don't have any experience with it and am unable to give you accurate advice.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!