Settings not set after calling register_setting()

register_setting does not insert anything in the database. It’s supposed to be run in admin_init, not just on activation, and is for building options pages with the Settings API and handles things like sanitisation and permissions when saving options in the admin.

If you want to add some default option values to the database on activation, use add_option(). It will add the option and value to the database, but only if there isn’t already a value for that option:

function integrazione_liferay_activate() {
    add_option( 'integrazione_liferay_cron_enabled', 1 );
    add_option( 'integrazione_liferay_flush_permalinks', 0 );
    add_option( 'integrazione_liferay_last_timestamp', 0 );
    add_option( 'integrazione_liferay_csv_data', '' );
}