Actually, the ID connection status is indicated by a small blue dot on the Host icon. If the dot is, well, blue it means the connection is live and well. A grey dot means the Host cannot connect to an intermediary server (whatever is set - public or private, in the Settings).
But if you just need information about the server on that tooltip as well, I think it might possible to add. I will send this suggestion over to our development.
Did you upgrade using Remote Install tool? If so, please re-download and re-install the Viewer https://www.remoteutilities.com/download/viewer6.5.msi . We updated the installer file yesterday without changing the version number because there a small issue with some files missing in the installation folder, and this prevented Remote Install from working properly.