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Messages sent by me are moved by a filter into a folder corresponding to the rexcipient's name under Local Folders.
Thunderbird marks these sent messages always wrongly as Unread.
Unfortunately this add-on can't resolve this annoying quirk.

Have you tried turning the option "Use different event to detect new messages" on? By default the addon listens to incoming mail event sent by Thunderbird. If you enable the option in addon settings then the addon listens to two events - when folder info is changed and when messages are moved. This should solve your problem.
UPDATE: From the discussion on github issue this is probably due to a bug in Thunderbird itself. The built in 'mark as read' action available in filters was not working for these messages and user was hoping that an addon would use a different system for marking messages as read - https://github.com/memeller/thunderbird-mark-as-read/issues/16