St. Paul insists on his being of the tribe of Benjamin, but I think he may sometimes include himself among "the Jews." St. Luke has him doing so in a speech at Acts 21.39 and 22.3.
Supposedly the term used until then meant a person who lived in Judea,many of them were from the tribes of Judah and Benjamin with some priestly Levites in the mix. The word used to describe them was Iudeceans and was so clumsy and awkward that the translators decided to use the term Jew.
In Judea there were also Greeks,Romans and various and sundry others and the term was not exclusive to the Old Testament religious Israelites from the tribes of Judah and Benjamin.
Since Jesus said He came to find the lost sheep of the tribes of Israel I think it's probable that multitudes can and are the lost sheep who traveled to other lands,were conquered during wars,lost the faith and,or were assimilated into other nations and culture.
I think we will all be much better off when this dawns on mankind.