thank you for the better screenshot. As you can see in the error message, the Gantry framework is trying to create a folder that already exists.
My hunch is that they're compiling the assets for your site (CSS, JS, twig template etc etc) but they're not checking if the folder they're going to use already exists, blindly creating them. If that folder is already there, an error occurs.
This is something not related to Akeeba Backup, since 95% of the code is related to the backend, the remaining it's for CLI operations or frontend backups which do not even require the template to load.
You should report this issue to Gantry developers, since it's not related to our software.
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