Tower of Babylon location is irrelevant to the religion of Babylon being used worldwide for thousands of years. It's the same eagle, deal with it dude. No matter how much you larp, cry, and seethe, that eagle is from the religion of Babylon.. even Saladin was fuckin' the king of Babylon area / Iraq, even the mainstream narrative says this, including the Wikipedia page:
"The Saladin eagle, originally from the Ancient Egyptian eagle shown in temples, the eagle became an important bird to Saladin. The Sultan of Egypt took the eagle as a symbol of his reign."
"Chariton has shown that the use of the double-headed eagle motif followed the westerly route from Mesopotamia to Anatolia sometime at the beginning of the 2nd millennium BC. That is because we have a Babylonian seal impression, probably from the third millennium BC, which displays a double-headed eagle over a king."
"Saladin (born 1137/38, Tikrīt, Mesopotamia [now in Iraq]—died March 4, 1193."
Quite literally NOTHING to show contrary to this eagle being from Babylon, you have LITERALLY no sources, and the Saladin eagle, which originated from Babylon, has been used by hundreds of civilizations and countries since, including Rome, Nazi Germany, and the United States.. fuckin' deal with it.