Is it established in an authentic hadith from the Prophet (peace and blessings be upon him) that the Basmala is recited aloud?

The Shaykh : I say the same: If the Messenger of Allah (peace and blessings be upon him) had done what the Shafi'is do today in every prayer, in every prayer, in every prayer—where it is necessary to recite the Basmala aloud, my brother—then the motivations would have been present to transmit this recitation aloud, just as they transmitted the recitation of Surat al-Fatihah aloud. Indeed, they transmitted from the Messenger (peace be upon him) that Abu Qatadah al-Ansari said, as in "Sahih al-Bukhari and Muslim": "The Messenger of Allah (peace and blessings be upon him) would sometimes let us hear the verse in the Zuhr and 'Asr prayers." These are prayers of silence, yet he let them hear the verse, meaning he recited it aloud so they could hear it. So why is there no valid transmission from any of them that the Messenger (peace be upon him) was always and forever reciting the Basmala aloud? This is practical evidence for the invalidity of what is attributed to the Messenger (peace be upon him) regarding his reciting the Basmala aloud. Despite all this, and after clarifying this reality—that the established Sunnah from the Prophet (peace and blessings be upon him) is to recite Surat al-Fatihah quietly—I say: We see no objection to the imam reciting the Basmala aloud occasionally among people who do not know the legitimacy of reciting the Basmala before Surat al-Fatihah. As I mentioned to you earlier, the Prophet (peace and blessings be upon him) would let his Companions hear the verse he recited after Surat al-Fatihah in Zuhr and 'Asr. And as is established from 'Umar ibn al-Khattab (may Allah be pleased with him) at the beginning of the prayer, the opening supplication, he would raise his voice. Why? To teach the people. So, raising the voice in a silent prayer for the purpose of teaching those who need to learn is not an objection. However, making it a system and a consistent rule to recite the Basmala aloud is contrary to the Sunnah.