Ethnicity seems to me to be a sort of taxonomic hierarchy. Some ethnic groups are more closely related to each other than others. Ethnicities can be grouped together into families of closely related ethnicities, which in turn can often be further grouped into broader families of less closely related ethnicities; ethnicities can often be further subdivided into sub-ethnicities. Are Jews a single ethnicity, or a family of related ethnicities? You could ask the same question about the Han Chinese, or about Italians; it is somewhat arbitrary, and the question is influenced by politics – Italian nationalism emphasises the notion of a single Italian ethnicity, separatist movements such as Sicilian nationalism or the Lega Nord emphasise regional ethnic identities instead.

You want to focus on subjective questions of identity, but it isn't clear to me that all Jews have the same subjective sense of identity. Does a secular Zionist in Tel Aviv have the same subjective sense of identity as a Satmar anti-Zionist in Kiryas Joel? Certainly their "subjective sense of identity" has completely different ideological foundations. They likely wouldn't agree on who is a Jew either, since their different ideological foundations would lead them to different positions on issues such as conversion standards and patrilineal descent.