Your new web server is ready to use

That isn’t the problem here at all.

Your server doesn’t have two external IP addresses, it has two IPs in different networks. The first (172.x) is part of a private IP range and it isn’t addressable externally.

The second is the public IP assigned to your server. Your applications are correctly attached to the externally addressable IP.

To make this work you’re going to need to proxy Discourse behind the other web server, there are guides here on meta on doing this. For now I would disable the other web server and focus on getting Discourse running to your satisfaction, then configure the proxy.