Firetray not support IMAP
In Firetray, I have IMAP support checked, but the tray does not show the icon. An email box moved from POP3 - drag drop method.
Wšě wotmołwy (1)
The add-on site https://addons.mozilla.org/en-US/thunderbird/addon/firetray/ says the support site for the add-on is. https://github.com/foudfou/FireTray/issues I suggest you seek support there.