Archaeological evidence of prehistoric human settlement on the island of Sardinia is present in the form of nuraghes and other prehistoric monuments, which dot the land. The recorded history of Sardinia begins with its contacts with the various people who sought to dominate western Mediterranean trade in classical antiquity: Phoenicians, Punics and Romans. Initially under the political and economic alliance with the Phoenician cities, it was partly conquered by Carthage in the late 6th century BC and then entirely by Rome after the First Punic War (230 BC). The island was included for centuries in the Roman province of Sardinia and Corsica, which would be incorporated into the diocese of Italia suburbicaria in 3rd and 7th centuries.
The paper actually says this about the Iceman: His phonotype shows “light skin pigmentation” (Table S10), with a score of 0.591 (Table S11), slightly higher than present-day Europeans (0.589), with the closest genetic affinities to Sardinians: https://www.cell.com/cms/10.1016/j.xgen.2023.100377/attachment/10edf088-8aae-401a-aaa6-ce990c25a646/mmc1
In the Early Middle Ages, through the European barbarian movements, the waning of the Byzantine Empire influence in the western Mediterranean and the Saracen raids, the island fell out of the sphere of influence of any higher government; this led to the birth of four independent kingdoms called Judicates (Latin: Judicati; Sardinian: Judicados) in the 8th through 10th centuries. Falling under papal influence, Sardinia became the focus of the rivalry of Genoa, Pisa, and the Crown of Aragon, which eventually subsumed the island as the Kingdom of Sardinia in 1324. The Iberian Kingdom was to last until 1718, when it was ceded to the House of Savoy; from Piedmont, the Savoyards pursued a policy of expansion to the rest of the Italian peninsula, having their Kingdom of Sardinia be later renamed into “Kingdom of Italy” in 1861.