这样修改源码来获取当前Webman当前执行的路由是否可行？

可行

上面的修改方案有问题，下面是新的修改方式。

修改类\Webman\App，如下

protected static function findRoute($connection, $path, $key, Request $request)
{
    $ret = Route::dispatch($request->method(), $path);

    if ($ret[0] === Dispatcher::FOUND) {
        $ret[0] = 'route';
        $callback = $ret[1]['callback'];
        $route = $ret[1]['route'];
        $app = $controller = $action = '';
        $args = !empty($ret[2]) ? $ret[2] : null;

        if (\is_array($callback) && isset($callback[0]) && $controller = \get_class($callback[0])) {
            $app = static::getAppByController($controller);
            $action = static::getRealMethod($controller, $callback[1]) ?? '';
        }

        $callback = static::getCallback($app, $callback, $args, true, $route);
        static::$_callbacks[$key] = [$callback, $app, $controller ? $controller : '', $action, $route]; // 将找到的路由对象缓存起来
        list($callback, $request->app, $request->controller, $request->action, $request->currentRoute) = static::$_callbacks[$key]; // 将路由对象复制到请求对象中
        static::send($connection, $callback($request), $request);

        if (\count(static::$_callbacks) > 1024) {
            static::clearCache();
        }

        return true;
    }
    return false;
}

public function onMessage(TcpConnection $connection, $request)
{
    try {
        static::$_request = $request;
        static::$_connection = $connection;
        $path = $request->path();
        $key = $request->method() . $path;

        if (isset(static::$_callbacks[$key])) {
            list($callback, $request->app, $request->controller, $request->action, $request->currentRoute) = static::$_callbacks[$key]; // 从缓存的数据读取相关信息并设置请求对象属性
            static::send($connection, $callback($request), $request);
            return null;
        }

        if (static::findFile($connection, $path, $key, $request)) {
            return null;
        }

        if (static::findRoute($connection, $path, $key, $request)) {
            return null;
        }

        $controller_and_action = static::parseControllerAction($path);

        if (!$controller_and_action || Route::hasDisableDefaultRoute()) {
            $callback = static::getFallback();
            $request->app = $request->controller = $request->action = '';
            static::send($connection, $callback($request), $request);
            return null;
        }

        $app = $controller_and_action['app'];
        $controller = $controller_and_action['controller'];
        $action = $controller_and_action['action'];
        $callback = static::getCallback($app, [$controller_and_action['instance'], $action]);
        static::$_callbacks[$key] = [$callback, $app, $controller, $action];
        list($callback, $request->app, $request->controller, $request->action) = static::$_callbacks[$key];
        static::send($connection, $callback($request), $request);
    } catch (\Throwable $e) {
        static::send($connection, static::exceptionResponse($e, $request), $request);
    }

    return null;
}

修改类\Webman\Http\Request，添加一个新的公共属性currentRoute来存储在应用中找到的路由对象，然后就可以使用$request->currentRoute来访问当前路由。

需要注意的是，webman在判断路由是否执行上面似乎并没有具体区分请求方法method，导致使用不同方法访问一个路由时，依旧会执行下去，在某些时候会报错，不过目前满足了自己的开发需要。

参照你的方案，已经支持通过 $request->route 获取路由信息，请更新。
composer require workerman/webman-framework ^1.3.2