Is the narration true which states that King Tubba' was the first man to believe in the Messenger Muhammad, may God bless him and grant him peace?

It is well-known that Abu Bakr, may Allah be pleased with him, was the first free man to believe in the Prophet, peace and blessings be upon him. This has been narrated by Al-Tirmidhi, Ibn Abi Shaybah, and Al-Hakim from a number of the Salaf, and it was preferred by Ibn Hajar, Ibn Taymiyyah, Ibn Kathir, and Al-Suyuti. As for the story of Tubba', Ibn Hajar mentioned in "Al-Fath" that he met four hundred rabbis in Yathrib who informed him about the Prophet, peace and blessings be upon him, and that he wrote a letter and enjoined that it be delivered to him. However, this does not mean that Tubba' was the first to embrace Islam; rather, the four hundred rabbis embraced Islam before him. The apparent meaning of the words of Ibn Hajar and Ibn Kathir indicates that Tubba' passed through Yathrib, which was an established city, and not one that was founded in his era.