Current behavior: as you know, TB is buggy especially with respect to connecting various mail servers (Gmail, Outlook, etc) so often there are random "Thunderbird: failure to connect to server" notifications. Also, sometimes I use TB offline to read emails, or in countries that block a email server (e.g. Gmail), so these failures ("Connection to server ... timed out") are expected and thus do not need raising.
These notifications can be distracting. I'd like to turn them off but I'd also like notifications for incoming emails. Right now there is no way to turn these notifications off without turning off all notifications.
Expected behavior: Thunderbird allows the user to decide which notifications are allowed to be raised.