Where are Author Layouts Stored?
The PublishPress Authors plugin stores the layout details in your site's database.
There is a custom post type called ppmacf_layout that holds the layout data. This means that you will find layouts in the wp_posts database table.
Here is a screenshot of data for the “Boxed” layout on the PublishPress.com website. You can see that the Twig code for the layout is in the post_content row.