Is the way that organs develop in embryos a relic of an evolutionary past?

Yes, its called comparative embryology. A chicken's embryo, a frog's embryo, a pig's embryo, and a human's embryo all look the same early in development, but as the embryo begins to develop they become more distinct, the human embryo looks a lot like a pig embryo up until the very end. This can show evolutionary history because humans and pigs are both mammals, so they will develop very similarly.