Are the two rak'ahs I prayed with the intention of the Sunnah of Fajr considered a supererogatory prayer, given that the call to Fajr prayer began while I was in the first rak'ah, or are they nullified as soon as I hear the adhan?

The two rak'ahs of Fajr are a sunnah (supererogatory prayer) performed before the obligatory Fajr prayer. It is not permissible to perform them except after their time begins with the appearance of true dawn (Al-Fajr Al-Sadiq). So, whoever performs them before that time, it is not sufficient, and they are obligated to repeat them after dawn breaks.