Legacy: SixOrNot, IPvFox provide IP addresses of servers accessed for building current page. SixOrNot (and maybe IPvFox?) also changes its toolbar icon to 4 or 6 to indicate if the top-level file of the page is connecting via IPv4 or IPv6.
Possible WebExtensions replacement: Show Server IP
Legacy: various host names in Title. This allows applications that need the server name for matching with site-specific logon credentials, such as for KeePass.
WebExtensions: Hostname in Title (There are probably others, too, but this was the first one I found.)