Localise settings section headline

Localize the headings in your initial array:

$sections = array(
    'notifcations' => __( 'Notifications', 'your_text_domain' ), 
    'updates' => __( 'Updates', 'your_text_domain' )
);

foreach ($sections as $section => $header )
{
    add_settings_section(
        $section .'_section',
        $header,
        array( $this, 'disable_callback_warnings' ),
        'sgnc'
    );
}