I'm not sure what I should look for. We know that the isle of Santorini is shaped by a large volcanic caldera and the usual date given for a huge volcanic eruption there is about 1600 BC. Hammurabi's reign is recorded to have ended circa 1750 BC.
Given the often indefinite dating of ancient events, I wondered if any controversy had arisen about Hammurabi's dates. Instead the controversy apparently centers on the Santorini eruption.
You say - The "supereruption" of the mid-2nd millennium is a modern invention. When did the elder crowd decide the volcano at Santorini erupted and what ended Minoan culture? ?:^|
19th century, even the Atlantis-was-Thera nonsense arose then, and it has been continually revived by various others for over a hundred years.
"Even when, during the respective Thera Conferences, individual scientists had pointed out that the magnitude and significance of the Thera eruption must be estimated as less than previously thought, the conferences acted to strengthen the original hypothesis. The individual experts believed that the arguments advanced by their colleagues were sound, and that the facts of a natural catastrophe were not in doubt... All three factors reflect a fantasy world rather than cool detachment, which is why it so difficult to refute the theory with rational arguments."The Future of the Past: Archaeology in the 21st Century by Eberhard Zangger, pp 49-50