Forgot to write a trigger to update poem_search.organ when an organ is updated. So, here it is (taken from a structure export):

DROP TRIGGER IF EXISTS `organ_update`;
DELIMITER //
CREATE TRIGGER `organ_update` AFTER UPDATE ON `organs`
 FOR EACH ROW BEGIN
    
    DECLARE organ_content text;

    CALL parse_organ(new.or_id, organ_content);
    UPDATE poem_search SET organ = organ_content WHERE id IN (SELECT po_id FROM poems WHERE po_organ = new.or_id);

END
//
DELIMITER ;