Is there a way after installing a new deployment forwarder to add it to a serverclass not from the server UI? can it be from client configurations/API?
YOu can update the serverclass.conf file on your new deployment server to add clients/apps/server class.
If you're looking for a way to update your client to connect to a deployment server, see this:
https://docs.splunk.com/Documentation/Splunk/7.2.5/Updating/Configuredeploymentclients