Yemen is also in Arabia. It's in the Southern portion of the peninsula. So at least some Jews in Arabia survived.
I think Jews had an independent kingdom in parts of Arabia at one time. Jews were also in Iraq and Syria long before Arabs were there. Arabs only conquered it after Mohammad. The Arabs were the interlopers and Arabized everyone they conquered besides Jews because Jews are a separate people from the Non-Jewish populations. Jews were in Iraq a thousands years prior to Arabs/Islam.
Probably Iraq is a made up term too just like Iran and Jordan. Iraq is really Babylonia and Iran is really Persia. Jordan is not only a made up term but the country is also made up like Fakestine.
Lebanon as a country is also made up. The Bible uses Lebanon as the name of a mountain range in Northern Israel. Syria seems to be more of a genuine country by name since it can be traced to Aram and Assyria. Syria was already used in the Hellenistic Period.
Egypt is not made up but the Arabization of it was.