something specifically for Thunderbird does not exist yet,but I have
seen that there will be an extension developed, when somebody does it.
Does not help you know, right.
But the free software suite from Eudora(email, webbrowser, conduits)
is able to make some of that what you want !!!!
The conduits will sync Thunderbird's mailboxes with the Eudora mail
application. The problem is ,that this free suit is from 2001 and lacks
some of the more modern feature. For example attachments, or html mails
are not supported.
But it works !
Ceck it out !
BTW, the address sync, the others gets so excited about, works for me