I'm wondering if at first Judaei and Ioudaioi would have had a geographical sense, all inhabitants of Judaea, and only later been restricted to adherents of the Jewish faith? In early Christian writings it's clearly a religious label, but I'm wondering if pagan Romans would have been careful in how they used the term. Of course there were Jews in Rome and in various provinces of the Roman Empire even before the destruction of Jerusalem. Tacitus in Histories Book 5 seems to use Judaei as a religious/ethnic term in his unfriendly and laughably ignorant discussion of the Jews. That was written a good deal after the destruction of Jerusalem.
In Esther, Mordechai identifies himself as of the Tribe of Benjamin and a Jewish man - ish Yehudi, presumably to clarify his allegiance to the Kingdom of Judah as opposed to being of earlier Exiles from the Northern Kingdom.
Jer. 34:9 KJV seems true to the Hebrew original:
“That every man should let his manservant, and every man his maidservant, being an Hebrew or an Hebrewess [Ivri and Ivriyah] go free; that none should serve himself of them, to wit, of a Jew [Yehudi] his brother.”