No....Anyone who migrated from the North to the Southern Kingdom of Judah also became known as a Jew. [II Chronicles 11:5-17] Rehoboam ruled in Judah 931/914 B.C. so understand that this was 200 years prior to the Assyrian exile. The people who remained in the North with their individual tribes were never called Jews.
FTD says that “Jew” and “Israelite” are interchangeable
They are if you are Jewish. The Jews were one of the tribes of Israel. This is like saying all Californians are American but not all Americans are Californians.
In your post #238 you said that some of the tribes migrated around the Black Sea. Perhaps these were the “Jews which were of Asia.” (Acts 21:27)
[1 Peter 1:1-2] shows that there were folks living in this area who had a foreknowledge of God and Peter is evangelizing them as he was instructed to do in [Matthew 10:5-6]. This is conjecture on my part....but they were probably a remnant from the Assyrian exile 700 years before. The reason I believe this is because that was part of ancient Assyria and Peter is doing what he is supposed to be doing! The Apostle Paul is actually told to stay out of here [Acts 16:6-7] as they were not his responsibility. They were not Jews....they were definitely not Gentiles....they were probably Israelites from the Ten tribes.
Would you argue that Passover is for just three tribes?
I would argue that Passover is for everyone who calls them self a Christian. We are no where in scripture told to ignore this Festival of the Lord. The last living Apostle, John....instructed his disciples to observe this as well.
From Polycrates of Ephesus: Regarding the celebration of Passover.
If Passover had been abolished by Our Lord don't you think the Apostle John would have received the memo?
There is nothing wrong with splitting hairs. Sometimes it leads to great discoveries.
Acts 21:27 And when the seven days were almost ended, the Jews which were of Asia, when they saw him in the temple, stirred up all the people, and laid hands on him,
Who were these "Jews of Asia?"