Rewriting url for multiple Taxonomies and Custom Post Type

You are specifying the same slug of lyrics for both your custom taxonomies. WordPress by default cannot share the same slugs for two taxonomies due to WordPress’ rewrite API. Which caters for the default nature of posts, archives, taxonomies, slugs and the WordPress template hierarchy.

To prevent your 404 errors you can change your artists array to a unique slug like so:

$args = array(
        "label" => __( "Artist", "sage" ),
        "labels" => $labels,
        "public" => true,
        "publicly_queryable" => true,
        "hierarchical" => true,
        "show_ui" => true,
        "show_in_menu" => true,
        "show_in_nav_menus" => true,
        "query_var" => true,
        "rewrite" => array( 'slug' => 'artists', 'with_front' => true,  'hierarchical' => true, ),
        "show_admin_column" => true,
        "show_in_rest" => true,
        "rest_base" => "artist",
        "rest_controller_class" => "WP_REST_Terms_Controller",
        "show_in_quick_edit" => true,
    );

Ensuring you flush your rewrite rules after doing so

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