Drupal - How to know add/edit page in hook_form_alter?

In D8 you can get the operation of an entity form with the form object:

function MYMODULE_form_alter(&$form, &$form_state, $form_id) {
  if ($form_state->getFormObject()->getOperation() == 'edit') {
    $page = 'edit';
  }
}

If you want to check for being on 'add' form, it is also possible to check that the entity is new, i.e.

function MYMODULE_form_alter(&$form, &$form_state, $form_id) {
  if ($form_state->getFormObject() instanceof EntityForm) {
    $entity = $form_state->getFormObject()->getEntity()
    if ($entity->isNew()) {
      //your code
    }
  }
}