Is this hadith authentic, what is its degree of authenticity, and what is its explanation if it is authentic?

The Hadith scholar Al-Albani discussed this hadith, stating that the narration "Who will guarantee my debts and my promises for me, and be with me in Paradise, and be my successor over my family?!" is weak due to the weakness of 'Abbad ibn Abdullah Al-Asadi and the poor memory of Shareek. As for the narration "Which of you will pledge allegiance to me to be my brother and my companion?!" its chain of transmission is good were it not for an unknown element in Rabi'a ibn Nakhib. The corroborating narration from Ibn Abbas, with the wording "Which of you will be my loyal supporter in this world and the Hereafter?" has an authentic chain of transmission and does not mention absolute succession.

In summary, the succession mentioned in this hadith is a specific succession over his family and clan. Imam Ibn Kathir explained that the Prophet's (peace be upon him) request to his uncles and their children to pay off his debts and succeed him over his family was out of fear that he might be killed in the cause of Allah before the verse (And Allah will protect you from the people) was revealed, and that Ali (may Allah be pleased with him) was quick to commit to what the Messenger of Allah (peace be upon him) requested from him.