That bit of lore is completely silly. Humans share a common ancestor with bananas if we go back far enough, and “The Chase” proposes to go back even further than that. Still a good episode, though.
However, nothing in Disco’s Klingon’s undoes that. We saw Klingon precursors when Worf was devolved into one in “Genesis” – another episode that has a Hollywood writer’s understanding of evolution – and he had an exoskeleton, mandibles, and spit acid.