Revisiting this civ after a long time, seeing the "Ask me Anything" post where someone says it's just a worst Korea. I used to like this civ in Vanilla, so it's painful to see it not being competitive in Science with other scientific civs. Notably with Korea, as both civs were considered to be main rivals for a Scientific Victory.
One note is the timing of the free scientist. In Vanilla, Writing was an Ancient Era technology that only required 1 tech (Pottery), while in VP, it's a Classical Era technology that requires 5 (Trapping, Pottery, The Wheel, Trade, Calendar). That means the free academy isn't necessarily worse due to yield adjustment, but due to how far later it comes, losing all of its impact. In Vanilla, it would double or triple one's science output when planted; in VP, it won't likely be even a 50% increase.
Similarly, the tech unlocking the UB requires only 1 tech in Vanilla (Mining), but 2 in VP (Mining, Animal Husbandry). The original UB didn't have the extra science that it has now, but it didn't meant Babylon had to delay its technologies away from Writing's prerequisites in order to have an early unique source of science. Babylon could beeline Writing and use the free academy to quickly reach the UB with little opportunity cost. This cost is greatly increased in VP.
Compared to Korea, there's also the Tradition branch giving access to multiple specialist slots with no production cost, allowing Korea to benefit from it's UA long before Babylon has access to its free scientist. In Vanilla, Babylon would have a free academy by the time Korea starts building its first building with a specialist slot (Library). The extra +15%

GP generation on Tradition also helps Korea in closing the GS generation of Babylon, as it stacks additively. Tradition Korea in a Golden Age (+45%) is pretty close to Babylon's UA, even if Babylon also chooses Tradition. Given that there are more sources of +X%

, a +50%

GS isn't as impressive as it used to be.
Overall, I think Babylon suffers from the delayed timing it got in VP, while its rivals were sped up. The extra GS generation is less relevant with the extra sources of

GP in the game, and noticeably challenged by the added +30%

GP during golden ages of Korea.