Can humans' ability to dive with only breathing modifications tell us anything about our evolution?
This is not a complete answer to your question, but your question prompted me to research the Mammalian Diving Reflex, which is used, according to the article, as a survival mechanism rather than assisting us in day to day functioning.

Looking at the evolution of the diving reflex, and how it appears in varying degrees in all mammals, suggest that it has been around for a long time, this article suggests for over 125 million years.