Should the public IP for my NAT be configured on my server?
The public IP for the NAT should NOT be configured on the server. The server should only be configured with the private IP of the NAT. The public IP for the NAT will exist in the firewall or other networking equipment that establishes the NAT.
To check if your server has been configured correctly, you can use the following command to list the server's IPs. It should contain the private IP of the NAT, but not the public IP of the NAT.
ip -o a
Note that the public IP for the NAT will be displayed in most parts of cPanel/WHM instead of the private IP of the NAT, such as "List Accounts" for example.