Is it established that the Prophet, may God's prayers and peace be upon him, used to recite Surat Qaf on Fridays?

It is established that the Prophet, peace and blessings be upon him, used to recite Surah Qaf — either all of it or part of it — every Friday. This is based on what was narrated by the daughter of Harithah ibn al-Nu'man, who said: "I did not memorize Surah Qaf except from the mouth of the Messenger of Allah, peace and blessings be upon him, reciting it in his sermon every Friday, and our oven and the oven of the Messenger of Allah were one." Some scholars have inferred the desirability of reciting Surah Qaf, or part of it, every Friday, in emulation of the Prophet, peace and blessings be upon him. Al-Nawawi mentioned the reason for choosing it was its inclusion of resurrection, death, and severe admonitions. Al-Tibi said: "What is meant is the beginning of the Surah, not its entirety." Al-Qari said: "It is not preserved that he recited its beginning every Friday; rather, it appears that he used to recite part of it." Ibn Uthaymin clarified that the Prophet, peace and blessings be upon him, used to preach with Surah Qaf and add to it: "To proceed: The best speech is the Book of Allah, and the best guidance is the guidance of Muhammad, and the worst of affairs are their innovations."