How authentic is the Hadith: "This is a hand loved by Allah and His Messenger"?

Firstly, the statement circulating among many writers, claiming that the Prophet (peace be upon him) kissed a man's rough hand due to work and said, "This is a hand that fire will never touch," lacks any authentic chain of narration. It has been narrated with a different wording in "Tarikh Baghdad," stating that the Prophet (peace be upon him) shook hands with Sa'd ibn Mu'adh al-Ansari after the Battle of Tabuk. When he saw the roughness of his hands, he asked him about it, and the man replied that he worked to provide for his family. The Prophet (peace be upon him) then kissed his hand and said, "This is a hand that fire will never touch." However, Al-Khatib al-Baghdadi clarified that this hadith is false because Sa'd ibn Mu'adh had already passed away before the Battle of Tabuk, and one of its narrators, Muhammad ibn Tamim al-Firyabi, was a liar who fabricated hadiths. Most scholars have agreed on the weakness and invalidity of the chains of narration for this story.

Secondly, working and striving with one's hands to provide for one's family, to give charity, and to protect oneself from begging, is a righteous deed for which a Muslim is rewarded. It is considered better for a person than asking people for help, as the Prophet (peace be upon him) said: "For one of you to take his rope and come with a bundle of firewood on his back and sell it, and Allah preserves his face with it, is better for him than asking people, whether they give him or refuse him." A Muslim strives to earn a lawful living for himself and his family, making it an act of closeness to Allah Almighty, in accordance with the Prophet's (peace be upon him) saying: "No one has ever eaten a better meal than that which he has eaten from the work of his own hand, and indeed, the Prophet of Allah, Dawud (peace be upon him), used to eat from the work of his own hand."