It’s in Typescript and builds to dist directory. The server is on dist/server.
I ran netlify init but it does not automatically detect/generate netlify.toml. Frankly I’m not sure how to configure it. Is there any example of similar projects deployed on Netlify Functions that I can use as reference?
I checked the docs but this guide is marked as outdated: Deploy to Netlify
This dist directory is that you will publish. Note that you cannot run a server on Netlify (the documentation you linked to mentions running the backend on Heroku or other such service.)
Documentation for netlify.tomlavailable here. In its simplest form you might only specify a build command and publish directory