Good job with the output. Based on that information, I do not see an app running on port 3000, localhost or otherwise. If you look at the lines you do provide, you can see an example of a localhost only app and an app that is publicly accessible (firewall notwithstanding):

Localhost only, postgres:
tcp 0 0 127.0.0.1:5432 0.0.0.0:* LISTEN 32442/postgres

The relevant info is the 127.0.0.1 which is the localhost IP address.

Publicly accessible, sshd, so you can connect:

tcp 0 0 0.0.0.0:22 0.0.0.0:* LISTEN 991/sshd

The relevant info there is the IP address before the port :22, 0.0.0.0 - that means it is listening on all interfaces on your droplet, local and public.

Try starting your app and running that command again - we should see a line that has :3000 and ruby in it. If it is bound to 127.0.0.1:3000 that is localhost only.

At that point you can either change your app config to bind to your public IP (or all interfaces) or, and this is a common solution, you run a proxy in front of the app like nginx.

Let us know how it goes and good luck!