Today there are two seemingly mutually exclusive notions of what “the Jews” are: either a religion or a nation/ethnicity. I want to find the biblical definition. Any suggestions?
there are two seemingly mutually exclusive notions of what “the Jews” are: either a religion or a nation/ethnicity
These are not mutually exclusive, one is close to being a subset of the other. The Hebrew Bible is not into providing definitions - that is a modern, Western thing. I would instead concentrate on Biblical indications of who is bound by the (Mosaic) law or who is covered by the Abrahamic covenant.
Today there are two seemingly mutually exclusive notions of what “the Jews” are
Read Dan 9:6-19 and ask yourself who are "your people" in Dan 9:24 and what is Judaism?
Judah was one tribe. The nation was originally 12 tribes, named after 12 sons of Jacob. There was a long history there and two northern tribes split off. At the time the New Testament was written, 10 of the original tribes had been scattered And we’re called “lost tribes”. The term “Jew“ at some point became used as a title of any of the 12 tribes. I do not know exactly how that happened, but the Apostle Paul refers to himself as a Jew, even though he was of the tribe of Benjamin.
So any of this could be used as a starting point for your study. A detailed English dictionary, such as the OED would probably give you an extensive etymology of the word itself. I’m pretty certain Logos does not have the full OED, they have an extremely abridged version of it.
Word studies of the Greek and Hebrew words might also give you quite a lot of history If you have TDNT or other theological dictionaries.