The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. 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.
3. 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'.

Optimal indexes for this query:

ALTER TABLE `order` ADD INDEX `order_idx_store_id` (`store_id`);
ALTER TABLE `order_line_item` ADD INDEX `order_item_idx_order_id_code_alternativ` (`order_id`,`code`,`alternative`);

The optimized query:

SELECT
        oli.*,
        oli2.* 
    FROM
        
    order o LEFT JOIN
        order_line_item oli 
            ON oli.order_id = o.id 
    LEFT JOIN
        order_line_item oli2 
            ON oli2.id = (
                SELECT
                    oli3.id 
            FROM
                order_line_item oli3 
            WHERE
                oli3.order_id = o.id 
                AND oli.code = oli3.alternative 
            GROUP BY
                oli3.code,
                o.id 
            ORDER BY
                NULL LIMIT 1
        ) 
    WHERE
        o.store_id != 100 
    GROUP BY
        oli.code,
        oli2.code,
        o.id 
    ORDER BY
        NULL