CPT is simply not displayed in the main archive with “pre_get_posts”

Okay, this is what works for me, thanks to the friendly hint of Jacob Peattie:

function include_custom_post_type_archives($query)
{
    if (is_home() && empty($query->query_vars['suppress_filters'])) {
        $query->set('post_type', array(
            'post', 'landingpages',
        ));
        return $query;
    }
}
add_filter('pre_get_posts', 'include_custom_post_type_archives');