It would appear that having the online offline status in the status bar is no longer appropriate, so I suggest that some other visual indicator of the current online status be provided.
Extra points if the indicator actually raises some sort of issue that the user can see if Thunderbird can not connect to its own servers' indicating either offline or software blocking.
Thunderbird needs to become proactive in informing the user of apparent issues. Instead of quietly deleting the entire folder structure of an IMAP account and every email in it because of a firewall issue.