To get beyond this problem, in the hosts file on the primary Process Automation server, we added the IP address for a load balancer that was not having network issues with the hostname of the load balancer we are trying to connect with as:
So that the URL check will attempt the connection using 10.10.25.25 and get a positive response. In this case, the webpage is unavailable is a positive response vs unable to resolve.
From there, the upgrade continued, and the setting in the hosts file was removed after that check had passed.
It's key to remember to remove the update in the hosts file before the primary node is started.
No changes are required to move forward with the upgrade of the secondary node or nodes.