What is the authenticity of the hadith of Abu Hurayrah: (When you recite al-Hamdu lillahi Rabbil 'Alamin, recite Bismillahi al-Rahman al-Rahim)?

The student: ... from Abu Hurayrah that the Prophet (peace and blessings be upon him) said: When you recite ...
The Shaykh : This hadith is not authentic; this hadith is not authentic. And that is indicated by the established hadith of Abu Hurayrah in the Sahih, in which Allah the Exalted said: to the end of the hadith. So He began with His saying: .
Second: The Messenger (peace and blessings be upon him) did not recite it aloud in the loud recitations, according to the stronger opinion. And if it were part of al-Fatihah, he would have recited it aloud just as he recites the rest of the verses aloud.
Third: The Basmalah is not part of the other surahs of the Qur'an, so we need strong evidence to clarify that it is part of al-Fatihah.
Fourth: His saying, the Exalted: is half in context and half in meaning, and that does not hold if we make the Basmalah part of it. Listen: This is for Allah, for Allah, three verses, for the servant, for the servant, for the servant. So: three and three, became between them as it came in the hadith , so it became three and a half verses for Allah and three and a half verses for the servant. And if we said that the Basmalah is part of it, this would not be consistent.
Fifth: If you make the Basmalah part of al-Fatihah, the last verse becomes long and does not correspond to what comes before it, because it will be the last verse , and this does not correspond to His saying: or . So it is contrary to eloquence. Thus, we have four aspects, all of which indicate that the Basmalah is not part of al-Fatihah. Yes.