While egypt tended not to interact with many other kingdoms- aside from the aforementioned Nubia/Kush, they were well aware of them and their political influence in the Eastern Mediterranean. The traded with the Greeks and their precursors the Myceneans- though originally they only ever bought olives, since that was the only thing that they produced- up until the Hellenic era after Alexander the Greats conquest. Otherwise they considered the Greeks as little better than pirates they occasionally got olives from. The traded more with the Phoenecian city-states of the levant, who were the earlier masters of the Mediterranean- the Egyptians at different periods even owned the Levant and it's trade-networks themselves.
They were also aware of Mesopotamia, and considered them a sister culture- despite having opposite worldviews, but looked down on them for their instability- and would be rarely threatened by any unified Mesopotamia that would briefly emerge.
They also bordered and at different times owned Judea- and like the rest of them considered them bizarre irrelevant zealot herders (there wasn't much urbanization of Judea- which is why you see constant shepherd metaphors in the bible- and Jerusalem as a city wasn't all that strong or wealthy).
They had much influence over the Kingdom of Cyrenaica however- now part of Libya, which had been settled by greek colonists, and sat on a relatively green plateau.
A big one of course is Persia, which would conquer the Levant, Anatolia, and Egypt- but pretty much everyone who wasn't greece (notably the jews who never had anything nice to say about anyone) really admired the persians not just for their wealth and power, but also their tolerance and the fact they didn't bother changing much when they conquered places.