Migrating a Drupal Node.js website from localhost to web server
The typical NodeJS setup usually involves a Linux server and a nginx web server/proxy that delegates the requests to the application running on a specific/semi-random unprivileged port. In other words, nginx will have a site declaration (vhost) for your Drupal and a another site declaration for your NodeJS application. Your NodeJS application runs in the backgrounds and listens for requests from nginx.

NodeJS itself is usually installed through the Linux distribution's packaging system, similarly to PHP.

On the filesystem, I would treat the two applications as separate projects, in two separate directories on the server. It's pretty rare to find developers who have a good understanding both Drupal/PHP and NodeJS, so keeping it separate will make it easier for other people eventually working on that project to familiarize themselves with the environment.