Is there an authentic Hadith from the Prophet (peace be upon him) indicating that the lands of the Gulf will become green and prosperous, while the lands of Sham (the Levant) will suffer from scarcity of rain and drought?

Perhaps the questioner is referring to the authentic hadith narrated by Muslim and others, that the Messenger of Allah, peace and blessings be upon him, said: "The Hour will not be established until wealth becomes abundant and overflows, to the extent that a man will go out with the zakat of his wealth and find no one to accept it from him, and until the land of Arabia returns to being meadows and rivers." And in another narration: "And until al-haraj becomes abundant." They (the Companions) asked: "What is al-haraj, O Messenger of Allah?" He said: "Killing, killing." The hadith did not mention the Gulf countries specifically, but they are included within the land of Arabia. We have not come across a hadith specifically indicating what you mentioned about the land of Sham (Greater Syria) being afflicted by drought. Rather, a hadith has been reported indicating that the city of Damascus in Sham will be among the best abodes for Muslims during the time of the Great Battle (al-Malhamah al-Kubra).