cara mengoptimalkan kueri ini (tabel 4 mm terlibat)

Anda harus menyingkirkan GROUP BY di sini.

MySQL kurang baik dalam mengoptimalkannya.

Tulis ulang kueri Anda seperti ini:

SELECT  *
FROM    product_table
WHERE   EXISTS
        (
        SELECT  NULL
        FROM    product_table__category_1__mm mm_1
        JOIN    category cat_1
        ON      cat_1.uid = mm_1.uid_foreign
        WHERE   mm_1.uid_local = product_table.uid
                AND mm_1.uid_foreign IN (7, 8)
        )
        AND
        …        

Buat indeks:

product_table__category_*__mm (uid_local, uid_foreign)

atau, lebih baik, nyatakan PRIMARY KEYs di product_table__category_*__mm :

ALTER TABLE product_table__category_*__mm ADD CONSTRAINT pk_pc*mm_local_foreign (uid_local, uid_foreign)