How does the Shafi'i school permit the slaughter of the sacrificial animal before the day of Eid, despite the Quranic command: "So pray to your Lord and sacrifice," which links prayer with sacrifice, and the Hadith: "Whoever slaughters before the prayer, it is only for himself"?

The fatwa you referred to did not mention the permissibility of slaughtering the Udhiyah (sacrificial animal for Eid al-Adha) before Eid according to the Shafi'i school. Rather, it mentioned the permissibility of slaughtering the obligatory Hady (sacrificial animal for Hajj) for pilgrims who find it difficult to keep it, once the first ten days of Dhul-Hijjah begin. As for the Udhiyah, it is not permissible to offer it before the day of Eid according to them. Its time for slaughter begins after sunrise on the Day of Nahr (Eid al-Adha), and after the time it takes to perform two short rak'ahs and two short khutbahs (sermons) has passed. Therefore, whoever slaughters before this time, their Udhiyah is not valid and becomes merely meat. The correct view among the Shafi'is is that the time for slaughtering the Hady is the same as the time for slaughtering the Udhiyah.