How does WordPress’s Recently Active Plugins list work?
Recently Active lists inactive plugins that have been deactivated in the last 7 days.

In wp-admin/plugins.php
line 212 the option “recently_activated” gets updated if a plugin is deactivated:

so the data is stored in the database table wp_options > recently_activated

The option contains an associative array containing the path to the main file of the plugin as the key and the time the plugins have been deactivated (as a UNIX timestamp) stored as a serialized value.
This data is rechecked each time you open the Plugins page in wp-admin before displaying the plugin table
The timestamp is used to determine the “recently active” plugins (wp-admin/includes/class-wp-plugins-list-table.php
line 188):
