Drupal - How to add extra arguments/parameters to ajax callback function?

Drupal doesn't have a mechanism to do that, no. As mentioned in the post you linked to, there's no need to pass that data to Javascript and then back to PHP though - just keep it in the form:

function mymodule_form($form, $form_state) {
  $form['button'] = array(
    '#type' => 'button',
    '#ajax' => array(
      'callback' => 'my_callback_function',
      'wrapper' => 'my_target_area',
    ),
  );

  $form['#foo'] = array($group1, ...);

}

function my_callback_function($form, $form_state) {
  $arguments = $form['#foo'];
  return $form['my_target_area'];
}

For pass data to ajaxCallback, this is how i do :

$form['repas'][$i]['detail']['midi']['mois_midi_'.$i] = [
              '#type' => 'select',
              '#title' => $this->t('Mois'),
              '#data'=>$i,
              '#options'=>array(
                  ''=>'Tous',
                  '01'=>'Janvier',
                  '02'=>'Février',
                  '03'=>'Mars',
                  '04'=>'Avril',
                  '05'=>'Mai',
                  '06'=>'Juin',
                  '07'=>'Juillet',
                  '08'=>'Aout',
                  '09'=>'Septembre',
                  '10'=>'Octobre',
                  '11'=>'Novembre',
                  '12'=>'Décembre',

              ),
              '#ajax'   => [
                  'event' => 'change',
                  'effet'=>'fade',
                  'wrapper'=>'legumes'.$i,
                  'method'=>'replace',
                  'callback' => array($this,'changeLegumeCallback'),
              ],
              '#default_value'=>$mois,
          ];

i add a custom attributes to my array : #data

Then in the callback :

public function changeLegumeCallback(array &$form, FormStateInterface $form_state){
    echo $form_state->getTriggeringElement()['#data'];
    exit();

}

You ll get your dynamic value from the trigger Element.