According to 23andMe this is northern West Asia:
Roughly bounded by Anatolia in the west to Iran in the east, northern West Asia has a shared genetic heritage going back tens of thousands of years. Domestication of grains and livestock emerged 11,000 years ago in this region, sparking the agricultural revolution that spread to parts of Europe, Africa, and other parts of Asia.
NW Asia
Ofcourse the Levant is part of the Middle Eastern world, but Levant is also part of the Semitic world and the Semites are southern West Asian people.
Neither genetically, nor culturally, Levantines/Semites such as Arabs are Jews are NW Asian people. The Levant people don't cluster together with NW Asian people (such as Kurds and the Georgians) on PCA charts. Their DNA is different.
Southern West Asian people = Semites (Arabs & Jews) from Arabia and Levant
Northern West Asian people = Caucasians, Anatolians and Iranians
Assyrians are in between. Semitic Assyrians/Chaldeans are a mixture of southern and northern West Asian people. Originally Semitic Assyrians/Chaldeans are from the Levant, but they are too much mixed with the native northern West Asian Mesopotamian people.