The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.
3. Replace Left Join With Subquery (modified query below): The pattern of inflating the amount of data (using joins) and deflating (using GROUP BY) usually slows down queries. In this case, it can be avoided by moving some of the logic to the SELECT clause, and therefore removing some of the LEFT JOINs. In some cases, this transformation can lead to an obsolete GROUP BY clause, which can also be removed.

Optimal indexes for this query:

ALTER TABLE `dia9__speedball_messages` ADD INDEX `dia9_speedball_idx_id` (`id`);
ALTER TABLE `dia9__speedball_tickets` ADD INDEX `dia9_speedball_idx_id` (`id`);
ALTER TABLE `dia9__speedball_tickets_messages` ADD INDEX `dia9_speedball_idx_ticketid` (`ticketid`);
ALTER TABLE `dia9__speedball_tickets_messages_mapping` ADD INDEX `dia9_speedball_idx_ticketmessageid` (`ticketmessageid`);

The optimized query:

SELECT
        DISTINCT a.ticketid,
        GROUP_CONCAT(tm.id) AS messageid,
        GROUP_CONCAT(tmm.messageid) AS ticketmessageid,
        (SELECT
            GROUP_CONCAT(mess.content) 
        FROM
            dia9__speedball_messages AS mess 
        WHERE
            tmm.ticketmessageid = mess.id LIMIT 1) 
    FROM
        `dia9__speedball_tickets` AS a 
    LEFT JOIN
        dia9__speedball_tickets_messages AS tm 
            ON tm.ticketid = a.id 
    LEFT JOIN
        dia9__speedball_tickets_messages_mapping AS tmm 
            ON tmm.ticketmessageid = tm.id 
    GROUP BY
        a.id 
    ORDER BY
        NULL