that's not true
Ethiopian Tewahedo, Coptic, and Assyrian orthodox churches have claims to apostolic succession and coexisted with the churches of Jerusalem/Greece/Rome
They "co-existed" at the same time. They were obviously aware of each other's existence and communicated. But the Ethiopian and Egyptian Coptic churches were NEVER under the authority of the church of Rome or Greece. They operated completely independently. Like the UN you can meet from time to time (only in that age "time to time" was measured in centuries rather than years) and try to come to agreements with each other, but the church of Alexandria and the church of Rome were founded by different people completely independently of each other, with the Alexandria church almost certainly founded first, and neither was ever under the other.
multiple schisms happened but don't kid yourself
they definitely linked and it doesn't take but a google search to see the imagery is obviously the same influence
You're saying artists in the Mediterranean world were vaguely aware of each other's existence while producing quite different styles and that shows....?
there literally is only a few differences like Miaphysitism and Duophysitism
which are more due to language reasons than doctrine. The whole "white" christianity is not true. The real issue is the reliance on the imagery to establish who Jesus is.
The Church of Alexandria and the Church of Rome were founded at different times by different people, but are originally based on the same divine person of Jesus, the same teachings of the Apostles, the same Gospel message and largely the same books of the Bible (none of which were written by Europeans). So obviously their theology will have the same root similarities. But the cultural outlook under which they were founded and evolved is completely different. From the beginning they operated in different languages, with different cultural emphasis and different theological frameworks. For a while they had a loose but usually friendly connection, then after the disputes in the 300s/400s they went 1500 years with virtually no connection at all.
Emphasizing that independence is important both cause of European whites who wish to claim Christianity for themselves and for non-whites who wish to dismiss Christianity as a White Religion. Yes, hopefully if you follow the same God and His prophets then you will have fundamental similarities. But African Christianity was not founded by Europeans, does not follow a European Jesus, and was never under Europe or relied on Europe for its understanding of itself and its relationship with God.