We would say: This is an innovation, because the Messenger ﷺ would recite an opening supplication only once, at the beginning of the prayer, (1) and it has not been reported from him that he repeated two different forms of the opening supplication.
“And seeking refuge, …”
His statement, “and seeking refuge,” means: except for seeking refuge—that is, saying, “I seek refuge in Allah from Satan, the accursed.” It is prescribed in the first rak'ah but not in the second, because the recitation in the prayer is a single recitation. The prayer is one act of worship from its beginning to its end; therefore, once he has sought refuge at the outset, that suffices.
For this reason, they said: If he recites a surah in the first rak'ah, then recites in the second rak'ah a surah that precedes it, this is disliked, as it goes against the established order—even if this occurs in the second rak'ah—because the recitation of the prayer is one recitation.
In al-Rawd (2), he says: “Unless he did not seek refuge in the first rak'ah, in which case he should seek refuge in the second.” This is a sound exception. An example is when one joins the imam while he is bowing: he will say the opening takbir, then say the takbir for bowing and bow. Thus, his recitation in the second rak'ah will be his first recitation, and at that point he should seek refuge.
What is stated in al-Rawd is, apparently, what they intended, for their reasoning indicates this, as they said: He seeks refuge before the first recitation. And the recitation of the prayer is one recitation.
Some scholars (3), however, held that one should seek refuge in every rak'ah, because acts of remembrance and physical actions come between the two recitations; therefore, he seeks refuge in Allah before reciting in every rak'ah.