What is the authenticity of the hadith that obliges moving a Muslim immediately upon death to face the Kaaba, and that the grave should face the Kaaba with the deceased's feet, knowing that the understanding is that the head or face should be directed towards the Qibla in the grave?

Directing the dying person towards the Qibla (Kaaba) during the throes of death is recommended, not obligatory, because there is no explicit textual evidence for it, nor is it reported that the Prophet ﷺ was directed towards it at the time of his death. As for placing the deceased in their grave, they should be laid on their right side, with their face towards the Qibla, and their head and feet positioned respectively to its right and left. This is what Muslims have traditionally practiced. The claim that people will emerge from their graves facing the Kaaba has no evidence; rather, what is established is that they will proceed directly to the Plain of Gathering.