Is it possible that the entire later Kingdom of Judea was made up of the descendants of the exiles who returned in the time of Cyrus? The returning exiles just could not have been that many, especially since many exiles, perhaps the majority, didn’t return at all; the exile community in Mesopotamia kept its identity long into the Christian Era.
Assyria carried the House of Israel out of there land and scattered them throughout the Assyrian empire in 721 BC.
2Kings was written around 550 BC, approximately 170 yrs. later. Let’s let SCRIPTURE answer your question.
(2 Ki 17:21 KJV) For he rent Israel from the house of David; and they made Jeroboam the son of Nebat king: and Jeroboam drave Israel from following the LORD, and made them sin a great sin.
(2 Ki 17:22 KJV) For the children of Israel walked in all the sins of Jeroboam which he did; they departed not from them;
(2 Ki 17:23 KJV) Until the LORD removed Israel out of his sight, as he had said by all his servants the prophets. So was Israel carried away out of their own land to Assyria unto this day.
and, many of the exiles would have stayed on in Iraq and become part of the population — just like how you had significant Jewish tribes in Mecca and Medina, so many present day Iraqis and Najaf Saudis would have partial descent from Judeans