Been wondering about this for a while... How does one "graduate" a notebook to an actual program on a server? Is there an actual standard procedure for that?

I'm pretty sure that if your notebook is big enough to debug what's in it you'd be doing everyone a disservice keeping it contained like that.

For a visual output, voila can give you a dashboard look: https://github.com/voila-dashboards/voila/ see e.g. https://github.com/maartenbreddels/voila-demo for a mobile-ready responsive rendering of a notebook.