How authentic is the Hadith about the king of India gifting the Prophet (peace and blessings be upon him) pickled ginger?

The narration about the King of India gifting ginger to the Prophet, peace and blessings be upon him, was reported by Al-Hakim, but it is well-known that the King of Rome was the one who gifted something to the Prophet, peace and blessings be upon him. This hadith was criticized by the scholars of hadith regarding Amr ibn Hakam, and he was accused of it due to his weakness. Al-Dhahabi denounced attributing the gift to the King of Rome and mentioned that the narration of Muhammad ibn Ashras is also not sound.

Ibn Abi Hatim mentioned that the known hadith is about the King of Rome gifting a cup [mustaqqah] of silk brocade, but this is rejected with the wording "sent it to your brother An-Najashi." The correct narration is that Ukaydir Dumah gifted the Prophet, peace and blessings be upon him, a silk brocade cloak. Ali ibn Zayd, the narrator of the hadith, is weak.