I think this question was answered a lot, but despite all threads I couldn't find a valid answer:

I'm working on a website with Wordpress (and without any plugin).

Here the creation of my custom post type 'actuality' and the taxonomy associated named 'actuality_type:

<?php

function create_actuality_taxonomy() {

    $labels = array(
        'name'              => _x( 'Type d\'actualité', 'taxonomy general name', 'textdomain' ),
        'singular_name'     => _x( 'Type d\'actualité', 'taxonomy singular name', 'textdomain' ),
        'search_items'      => __( 'Chercher un type', 'textdomain' ),
        'all_items'         => __( 'Tout les types', 'textdomain' ),
        'edit_item'         => __( 'Editer le type', 'textdomain' ),
        'update_item'       => __( 'Mettre à jour le type', 'textdomain' ),
        'add_new_item'      => __( 'Ajouter un nouveau type', 'textdomain' ),
        'new_item_name'     => __( 'Nom du nouveau type', 'textdomain' ),
        'menu_name'         => __( 'Type d\'actualité', 'textdomain' ),
    );

    $args = array(
        'hierarchical'      => true,
        'labels'            => $labels,
        'show_ui'           => true,
        'show_admin_column' => false,
        'query_var'         => true,
        'rewrite'           => array(
            'slug' => 'actuality', // This controls the base slug that will display before each term
            'with_front' => false  // Don't display the category base before
         ),
        'show_in_rest'      => true,
        'show_in_quick_edit'=> false,
        'public'            => true,
        'meta_box_cb'       => false,
        'show_in_nav_menus' => false,
        'has_archive'       => true
    );
    //first name of the taxonomy, second post_type name
    register_taxonomy( 'actuality_type', 'actuality', $args );
}

function create_actuality_custom_post_type() {

    $labels = array(
        'name'                => _x( 'Actualités', 'Post Type General Name'),
        'singular_name'       => _x( 'Actualité', 'Post Type Singular Name'),
        'menu_name'           => __( 'Ajouter une Actu'),
        'all_items'           => __( 'Toutes les Actualités'),
        'view_item'           => __( 'Voir les actualités'),
        'add_new_item'        => __( 'Ajouter une nouvelle Actualité'),
        'add_new'             => __( 'Ajouter'),
        'edit_item'           => __( 'Editer l\'Actualité'),
        'update_item'         => __( 'Modifier l\'Actualité'),
        'search_items'        => __( 'Rechercher une Actualité'),
        'not_found'           => __( 'Non trouvée'),
        'not_found_in_trash'  => __( 'Non trouvée dans la corbeille'),
    );

    $args = array(
        'label'               => __('actuality'),
        'description'         => __( 'Toute l\'actualité'),
        'menu_icon'           => 'dashicons-admin-site',
        'labels'              => $labels,
        'supports'            => array( 'title', 'editor', 'excerpt', 'author', 'thumbnail', 'revisions', 'custom-fields' ),
        'show_in_rest'        => true,
        'hierarchical'        => false,
        'public'              => true,
        'publicly_queryable'  => true,
        'menu_position'       => 4,
        'has_archive'         => 'actuality',
        'rewrite'             => array(
            'slug' => 'actuality/%actuality_type%', 'with_front' => false
        ),
        'capability_type'     => 'post',
    );

    register_post_type( 'actuality', $args );
}

Now, on my function.php file, this is how I implement those:

/*
 * Add the menu "Create News" and Custom post typr on the admin page
 */

add_action('init', 'create_actuality_custom_post_type', 0);

/*
 *  Register new taxonomy for Actualities: News, Event and Salon
 */

add_action('init', 'create_actuality_taxonomy', 0);

/*
 * Change permalink for actuality taxonomy
 */

function filter_post_type_link_for_actuality($link, $post) {
    if ( $post->post_type !== 'actuality' ) {
        return $link;
    }

    if ( $cats = get_the_terms($post->ID, 'actuality_type') ) {
        $link = str_replace('%actuality_type%', array_pop($cats)->slug, $link);
    }

    return $link;
}
add_filter('post_type_link', 'filter_post_type_link_for_actuality', 10, 2);

The menu appears on my administration page, I can create some 'actuality_type' like 'salons'.

Now, if I make a new 'actuality' with 'Salons for ever' as a title and I set the 'actuality_type' on salons, the permalink is: http://localhost/mywordpress/actuality/salons/salons-for-ever/

But i have a 404 on this link and I don't know why. I acted empirically by creating a lot of file like

actuality-salons.php actuality_type-salons.php archive-actuality-salons.php archive-actuality_type-salons.php page-salons.php page-actuality-salons.php page-actuality_type-salons.php single-actuality-salons.php single-actuality_type-salons.php taxonomy-actuality-salons.php taxonomy-actuality_type-salons.php But none works.

I already try to use flush_rewrite_rules( false ); or reload the permalinks on the settings.

Thanks a lot everyone

Have a nice day