Unfortunately, the IMAP IDLE extension only works with one mailbox at a time. This is a limitation in the protocol, and both Dovecot and Thunderbird are simply following the protocol. If I remember correctly, Thunderbird only uses IDLE for the INBOX. And while it is using IDLE, it cannot poll the other folders for new mail (well, I suppose it could come out of IDLE, poll all the folders, and go back to IDLE, but it seems like an ugly hack). So you can only use one of 2 modes: either use IDLE, and get notifications of new mail in INBOX only, or use normals periodic polls of all your folders to get notifications of new mail in all of them.
I may be mistaken, but doesn't 'ENHANCED_IDLE' work with not only multiple/concurrent connections to the same folder, but also multiple folders?
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Best regards,
Charles