I’d say that an Empire requires that the ethnicities remain largely separate afterwards - e.g the British and Indians didn’t meld into one nation, the Romans, Gauls, Iberians, Greeks etc didn’t form one Roman Imperial ethnicity. But post-unification, there was just one Egypt - that’s not an Empire, that’s a Kingdom (see: England, 1066->present)
The Akkadian Empire is the first empire because the Akkadians ruled over not just their own selves, but also other Semites and Sumerian peoples. Egypt only really achieved this level with the New Kingdom, when it exercised hegemony over the Levantine coast and Kush, AFAIK.
Religion doesn’t exclusively make ethnicity though - e.g individual Greek city-states had individual patron gods (Athena for Athens, Artemis and Ares for Sparta etc) but shared a culture/ethnicity - I’d want to know if there was a shared language between the two Egypts, and other cultural touchpoints. Which we may never know, I guess. But telling, for me, is the fact that there was total unification afterwards - that’s not an empire, that’s a new polity. Upper and Lower Egyptian ethnicities didn’t remain distinct AFAICT.