you've couched your thread in antisemetism and demanded a narrow answer to one of two instances of being carried away either to Babylon or Assyria, but the real question here is the same one of the book of Job, whether blessing & calamity are direct results of sin and righteousness -- and you have chosen the answer of Eliphaz, Bildad & Zophar, saying that Israel cannot be Israel because God never materially blesses the unrepentant or shows kindness to sinners.
this is wrong. God rebuked these men; He shows mercy to whom He will show mercy.
the sojourning of the people in Egypt is the sojourning of the people in Babylon, yes. it is the same. He treats Israel as his wife, Ephraim as His son, and these things are the same as the Levite who went to speak kindly to his wife in Judges 19:1-3 -- which is the same as Christ coming to pitch His tent among a people who reject the light. it is the same as king Josiah being prophesied and appearing, taking the throne among an idolatrous people who forsook God, and reforming them. the people did not tear their own high places down and take their own idols out of the temple and only then was Josiah sent, but Josiah was sent and did these things.
the people were cursing God, saying He only brought them out of Egypt in order to murder them in the wilderness, when He parted the Sea of Reeds. the people were cursing God, saying He only brought them out of Egypt to murder them, their children, and their animals when He gave them manna.
you said, the people were captives in Egypt for their good, as though this wasn't the case in Babylon. but God says the Babylonian captivity was for their good:
Thus says the LORD, the God of Israel: ‘Like these good figs, so will I acknowledge those who are carried away captive from Judah, whom I have sent out of this place for their own good, into the land of the Chaldeans. For I will set My eyes on them for good, and I will bring them back to this land; I will build them and not pull them down, and I will plant them and not pluck them up. Then I will give them a heart to know Me, that I am the LORD; and they shall be My people, and I will be their God, for they shall return to Me with their whole heart.'
(Jeremiah 24:5-7)
in fact ((see rest of chapter)) He says the people who were not scattered, are the bad figs, accursed. and look who it was who gave them a heart to know God? God Himself, not them themselves. it was not they who repented and caused God to change His judgement, but God who appointed their season of sojourning and who turned their hearts Himself.
your premise here is that Israel is not Israel because Israel is still blinded, fulfilling the Word which was spoken through Isaiah, until the bringing in of the Gentiles is complete. but these are His own appointed times and His own chosen people -- they were not brought out of Babylon because of their 'sovereign-free-will-choice' but because God appointed the years of their captivity, because God gave them a heart to know Him, and because God brought about both their sojourning and their gathering:
For thus says the LORD: After seventy years are completed at Babylon, I will visit you and perform My good word toward you, and cause you to return to this place. For I know the thoughts that I think toward you, says the LORD, thoughts of peace and not of evil, to give you a future and a hope. Then you will call upon Me and go and pray to Me, and I will listen to you. And you will seek Me and find Me, when you search for Me with all your heart. I will be found by you, says the LORD, and I will bring you back from your captivity; I will gather you from all the nations and from all the places where I have driven you, says the LORD, and I will bring you to the place from which I cause you to be carried away captive.
(Jeremiah 29:10-14)
seventy years. according to the Word of the LORD, not according to the whim of the people. according to the sovereign decree of God, not the sovereign will of man. He appointed the time of the people's exile & suffering in Egypt, and He appointed the time of their exile & suffering in Babylon, and He appointed the time of Job's suffering, and He appointed the time of yours and mine.
Eliphaz, Bildad, Zophar & Phoneman say if you are blessed you have been righteous, and if you have trouble you have sinned. you say, God does not bless His people and give them a home, a land, and a name, unless they are holy. you say, Israel is not Israel because Israel does not do the works you want to see them doing. but God says He creates the light and forms the darkness, brings goodness and calamity, and appoints the time and the seasons. God says He reveals Himself to a people who did not look for Him, that He comes to save sinners, to bind up the broken hearted and heal the sick, not the well.
you act like no one prayed in Auschwitz.