Ancient Egyptian is a Northern Cushitic language just like the Beja language which is also divergent from other Afro Asiatic languages. The Beja are from Egypt and they used to be known as the Medjay clan. They were considered Nubian at first, but then they slowly integrated into Egypt.
Ancient Egypt was surrounded by Cushitic languages from the East (Arabia), South (Nubia/Sudan) and South East (Punt).
"According to Peter Behrens (1981) and Marianne Bechaus-Gerst (2000), linguistic evidence indicates that the
Kerma (Nubia) peoples spoke Afro-Asiatic languages of the
Cushitic branch."
"The languages are spoken in the ancient Kerma Culture (present-day southern Egypt and northern Sudan) also belonged to the Cushitic branch of the Afroasiatic languages."
https://en.wikipedia.org/wiki/Kerma_Culture
"Additionally, Militarev identified a Cushitic substratum in Modern South Arabian,
which he proposes is evidence that Cushitic speakers originally inhabited the Arabian Peninsula alongside Semitic speakers (Militarev 1984, 18-19; cf. also Belova 2003). According to Václav Blažek, this suggests that Semitic peoples assimilated their original Cushitic neighbors to the south who did not later emigrate to the Horn of Africa. He argues that the Levant would thus have been the Proto-Afro-Asiatic Urheimat, from where the various branches of the Afro-Asiatic family subsequently dispersed. To further support this, Blažek cites the analysis of rock art in Central Arabia by Anati (1968, 180-84), which notes a connection between the shield-carrying "oval-headed" people depicted on the cave paintings and the
Arabian Cushites from the Old Testament, who were similarly described as carrying specific shields."
http://www.phil.muni.cz/jazyk/files/AAmigrationsCORR.pdf
Egypt's first King ruled from Nubia.
"Most surprising, evidence that early pharaohs ruled in A-Group Nubia was discovered by the Oriental Institute at Qustul, almost at the modern Sudanese border. A cemetery of large tombs contained evidence of wealth and representations of the rulers and their victories. Other representations and monuments could then be identified, and in the process, a lost kingdom, called Ta-Seti or Land of the Bow, was discovered. In fact, the cemetery at Qustul leads directly to the first great royal monuments of Egypt in a progression.
Qustul in Nubia could well have been the seat of Egypt's founding dynasty."
https://oi.uchicago.edu/museum-exhibits/special-exhibits/nubia-salvage-project-1
Adeer, Ethiopia stole its name from Sudan. Sudan's old names were Ethiopia, Kush, and Nubia.