Final Solution

Creating attributes with wc_create_attribute, and then we explicitly registering taxonomies solves the problem:

/**
 * Create a new global attribute if doesn't exist.
 *
 * @since 3.2.0
 * @param string $name | Name of the attribute.
 * @param string $label | Label of the attribute.
 */
function create_global_attribute($name, $label = '') {
    $attributes = wc_get_attribute_taxonomies();

    $slugs = wp_list_pluck( $attributes, 'attribute_name' );

    if ( ! in_array( $name, $slugs ) ) {

        $args = array(
            'slug'          => wc_sanitize_taxonomy_name( $name ),
            'name'          => ! empty( $label ) ? $label : ucfirst( $name ),
            'type'          => 'select',
            'orderby'       => 'menu_order',
            'has_archives'  => false,
        );

        $result = wc_create_attribute( $args );

    }
}

/**
 * Create a new variable product (with new attributes if they are).
 *
 * @since 3.0.0
 * @param array $data | The data to insert in the product.
 */
function create_product_variation( $data ){
    if( ! function_exists ( 'create_global_attribute' ) ) return;

    $postname = sanitize_title( $data['title'] );
    $author = empty( $data['author'] ) ? '1' : $data['author'];

    $post_data = [
        'post_author'   => $author,
        'post_name'     => $postname,
        'post_title'    => $data['title'],
        'post_content'  => $data['content'],
        'post_excerpt'  => $data['excerpt'],
        'post_status'   => 'publish',
        'ping_status'   => 'closed',
        'post_type'     => 'product',
        'guid'          => home_url( '/product/'.$postname.'/' ),
    ];

    // Creating the product (post data)
    $product_id = wp_insert_post( $post_data );

    // Get an instance of the WC_Product_Variable object and save it
    $product = new WC_Product_Variable( $product_id );
    $product->save();

    ## ---------------------- Other optional data  ---------------------- 
    ##
    ##     (see WC_Product and WC_Product_Variable setters methods)

    // THE PRICES (No prices yet as we need to create product variations)

    // IMAGES GALLERY
    if( ! empty( $data['gallery_ids'] ) && count( $data['gallery_ids'] ) > 0 )
        $product->set_gallery_image_ids( $data['gallery_ids'] );

    // SKU
    if( ! empty( $data['sku'] ) )
        $product->set_sku( $data['sku'] );

    // STOCK (stock will be managed in variations)
    $product->set_stock_quantity( $data['stock'] ); // Set a minimal stock quantity
    $product->set_manage_stock( true );
    $product->set_stock_status('');

    // Tax class
    if( empty( $data['tax_class'] ) )
        $product->set_tax_class( $data['tax_class'] );

    // WEIGHT
    if( ! empty( $data['weight'] ) )
        $product->set_weight(''); // weight (reseting)
    else
        $product->set_weight( $data['weight'] );

    $product->validate_props(); // Check validation

    ## ---------------------- VARIATION ATTRIBUTES ---------------------- 
    ##

    $product_attributes = array();

    foreach( $data['attributes'] as $key => $terms ){
        $taxonomy = wc_attribute_taxonomy_name( $key ); // The taxonomy slug

        // NEW Attributes: Create if doesn't exist and register taxonomy
        if( ! taxonomy_exists( $taxonomy ) ) {
            create_global_attribute( $key, $key );
            register_taxonomy( $taxonomy, array('product'), array(
                'type'    => 'select',
                'orderby' => 'menu_order',
                'public'  => 0,
            ));
        }

        $product_attributes[$taxonomy] = [
            'name'         => $taxonomy,
            'value'        => '',
            'position'     => '',
            'is_visible'   => 0,
            'is_variation' => 1,
            'is_taxonomy'  => 1
        ];

        foreach( $terms as $value ){
            $term_name = ucfirst($value);
            $term_slug = sanitize_title($value);

            // Check if the Term name exist and if not we create it.
            if( ! term_exists( $value, $taxonomy ) ) {
                wp_insert_term( $term_name, $taxonomy, ['slug' => $term_slug] ); // Create the term
            }

            // Set attribute values
            wp_set_post_terms( $product_id, $term_name, $taxonomy, true );
        }
    }
    update_post_meta( $product_id, '_product_attributes', $product_attributes );
    $product->save(); // Save the data
}

Regarding adding atributes in your code

The wc_get_attribute_taxonomies retrieves the last added attribute because you add the taxonomy incorrectly, namely you don’t register it but only insert directly to the DB, so the transient wc_attribute_taxonomies contains the last added attribute:

...
if( empty($attribute_id) ) {
    /**
     * New taxonomy inserts directly here 
     * without getting registered in $wp_taxonomies 
     */
    $wpdb->insert(  "{$wpdb->prefix}woocommerce_attribute_taxonomies", $args );
    set_transient( 'wc_attribute_taxonomies', false );
}

if( $set ){
    $attributes = wc_get_attribute_taxonomies();
    /**
     * Here $attributes containes the last attribute 
     * because the wc_get_attribute_taxonomies
     * fetches the cached value.
     * @see https://woocommerce.github.io/code-reference/files/woocommerce-includes-wc-attribute-functions.html#source-view.55
     */
    $args['attribute_id'] = get_attribute_id_from_name( $name );
    $attributes[] = (object) $args;
    set_transient( 'wc_attribute_taxonomies', $attributes );
} else {
    return;
}
...

You can fetch the attributes directly from the database as Woocommerce does in the mentioned function, so the code would be:

...
if( empty($attribute_id) ) {
    /**
     * New taxonomy inserts directly here 
     * without getting registered in $wp_taxonomies 
     */
    $wpdb->insert(  "{$wpdb->prefix}woocommerce_attribute_taxonomies", $args );
    set_transient( 'wc_attribute_taxonomies', false );
}

if( $set ){
    $attributes = $wpdb->get_results( "SELECT * FROM {$wpdb->prefix}woocommerce_attribute_taxonomies WHERE attribute_name != '' ORDER BY attribute_name ASC;" );
    $args['attribute_id'] = get_attribute_id_from_name( $name );
    $attributes[] = (object) $args;
    set_transient( 'wc_attribute_taxonomies', $attributes );
} else {
    return;
}
...

Regarding adding terms in your code

the wp_insert_term returns WP_Error when checks the taxonomy for this term exists. Even though you insert new taxonomy here:

$wpdb->insert(  "{$wpdb->prefix}woocommerce_attribute_taxonomies", $args );

as I said before, you do that directly, without registering it in $wp_taxonomies that’s why it doesn’t add new terms:

// Check if the Term name exist and if not we create it.
if( ! term_exists( $value, $taxonomy ) )
    wp_insert_term( $term_name, $taxonomy, array('slug' => $term_slug ) );
    /**
     * wp_insert_term checks the given $taxonomy exists using taxonomy_exists()
     * @see https://github.com/WordPress/WordPress/blob/5.8/wp-includes/taxonomy.php#L2280
     * in turn taxonomomy_exists() checks it within $wp_taxonomies
     * @see https://github.com/WordPress/WordPress/blob/5.8/wp-includes/taxonomy.php#L309
     */