Currently there is a lot of overlap between the sidebar and the tab bar in Thunderbird UI and therefore there should be a proper concept for it do define clearly what is for what.
The tab bar is an unified bar where everything has it's own tab, there is no separation between the core functions. So an opened e-mail tab sits next to the calendar tab.
In the meantime there is a sidebar that has dedicated buttons for each core function, mail, address book, calendar, tasks and chat.
It would make a lot more sense if the tab bar would only show the relevant tabs. So if the calendar is opened, its tab would only be visible if the calendar is selected on the sidebar. E-mail related tabs would be hidden. And if the e-mail is selected on the sidebar, calendar, tasks, etc. would be hidden then.
On top of that it would be nice if there would be an option to put each e-mail accounts into a dedicated tab rather than having them in a long long list on the left panel of the screen. Then that left panel could be shrinked to only show folder icons and it would reveal folder names on hover. Since then there would be only 1 account inside a tab it would make the left panel lot more simple.