As a rule, the target server runs on Linux. All of the major distros have systemd. You can use it to create a service for your tinyhttp app.
The most popular process manager for Node.js is PM2. It has a clustering feature built-in so it's very easy to make your app multi-process. However, using pm2 is not required to have clustering. You can do the same using the built-in cluster module. Check the cluster example for more info.