问题是，您正在从非静态方法内部调用静态方法。以下操作将起作用。

class theme_Rest_Routes extends WP_REST_Controller{

    public static function init() {
        $instance = new self();
        add_action( \'rest_api_init\', array( $instance, \'register_routes\' ) );
    }

    public function register_routes() {
        register_rest_route( \'theme/v1\', \'/menu/\', array(
            \'methods\' => \'GET\',
            \'callback\' => array( $this, \'theme_rest_menu\' ) )
        );
    }

    public function theme_rest_menu( $request ) {
        return wp_get_nav_menu_items( \'menu\' );
    }
}
theme_Rest_Routes::init();

代码改进rest_api_init 从控制器类本身内部，而不是从外部类/函数调用它。类名也应该使用大写单词。如下所示：

function theme_register_rest_apis() {
    $controller = new Theme_Rest_Routes();
    $controller->register_routes();
}
add_action( \'rest_api_init\', \'theme_register_rest_apis\' );

class Theme_Rest_Routes extends WP_REST_Controller{

    public function register_routes() {
        register_rest_route( \'theme/v1\', \'/menu/\', array(
            \'methods\' => \'GET\',
            \'callback\' => array( $this, \'theme_rest_menu\' ) )
        );
    }

    public function theme_rest_menu( $request ) {
        return wp_get_nav_menu_items( \'menu\' );
    }
}