Mail accounts are virtual, i.e. they don't have an actual account on the machine. Thus your account name should be accountName@domain.com
and the mail server name should be domain.com. So you would be actually logging into accountName@email@example.com in thunderbird. If after making the modification above you still see no auth attempts in the logs, try ensuring that you are connecting on port 25 in thunderbird's outgoing mail server settings.