500 internal server error/requested timeout at built project ip(/droplet) address

Can you check with curl from your droplet if your app is running?

curl http://localhost:1337

Replace with your host/port if they are different.
There is no need to use the server.js file. I would also recommend using pm2 to run your project in production by using ecosystem config:

  
module.exports = {
  apps: [
    {
      name: 'your-app-name',
      script: 'npm',
      args: 'start',
      env: {
        NODE_ENV: 'production',
      },
      exp_backoff_restart_delay: 100,
    },
  ],
};

Then you can check the logs with pm2 logs.
You can take a look at the useful tutorial from digitalocean on how to set-up a nodejs app with pm2, but instead of using the