Did our master, Omar ibn al-Khattab, bury daughters alive before Islam, or not, considering the contradiction between what was mentioned in the program "Our History in the Balance" and the series "The Prophetic Biography" regarding this?

The story mentioned has not been reported in the authenticated books, nor does it have any chain of transmission whatsoever. Scholars have also invalidated it from the perspective of its meaning. Furthermore, infanticide (wa'd) was not a widespread custom among the Arabs, nor was it prevalent in Banu Adi or the family of Al-Khattab. Hafsa was born five years before the Prophetic mission, and Umar did not bury her alive. So why would he bury the supposedly younger daughter alive? And why did her news disappear, and why did none of her relatives mention her?