We are making progress. You consent that the term Jew does not only refer to a Jew of the tribe of Judah, but whoever attaches himself to the nation of the Jews, ie., the Jewish People. All Israel, the remnant of Israel from each of the Twelve Tribes, in Exile or the Land of Israel, looked to Judea because therein lay Jerusalem, the eternal city where God placed His Name.
Mordechai was of the tribe of Benjamin, not the tribe of Judah. He was a Jew. There were many who saw the salvation of the Jews in the time of Mordechai and Esther and became Jews while in the Exile. And in every province, and in every city, whithersoever the king's commandment and his decree came, the Jews had joy and gladness, a feast and a good day. And many of the people of the land became Jews; for the fear of the Jews fell upon them.
Esther, Catholic chapter eight, Protestant verse seventeen,
as authorized, but not authored, by King James,
boldness mine
I’m not sure you’re making progress at all. This is really not hard.
The southern kingdom was composed of the tribe of Judah and the tribe of Benjamin. The tribe boundaries are described in detail in the book of Joshua, should you wish to check me.
When Israel split after Solomon’s death and the failure of Ish-Bosheth to unite the tribes, the ten northern tribes became Israel, and Judah and Benjamin became Judah, capital Jerusalem.
When the southern kingdom was conquered by Babylon, the captives were from both tribes, Judah and Benjamin. They (including Mordecai) became known as “Jews” because they were from the kingdom of Judah. When they returned to rebuild after the captivity, they were still Jews. When Jesus walked the land, they were still Jews. Benjamites and those of Judah, all Jews.
As for the 10 northern tribes, they were never re-united, never returned to the homeland, were assimilated and scattered and re-homed. They became mongrels, like the Samaritans. (Check the middle of II Kings for a description of their plight. I’m too tired to look it up for you.) Their descendants, assuming they have any knowledge of their genetics, would certainly be part physical Israelite, but they would not be Jews.
I, too, consider myself an ingrafted member of the spiritual Israelites, God’s chosen people. And I don’t have a drop of Semitic blood in me.