Is it possible to group plugins into a folder?

Short answer is no.

WordPress defines plugin paths allowing plugins authors to use plugin content functions to locate their files, and these are controlled by the WordPress content constants which are set in the file

wp-includes/default-constants.php

However, although the path are customisable, WordPress only searches this one location. The only exception to this is network installations which have an extra folder muplugin which WP will scan for must-use plugins.

WordPress calls the function wp_get_active_and_valid_plugins to load plugins at run time, but does not provide any hooks to modify the loading process.