There isn't a straight answer... yet.
The first step is to separate what we actually know about which functions are where from the vast amount of left brain/ right brain pseudoscience that's out there.
And the second is to look at how it works in other organisms. Here's a Scientific American article from 2009 which I think isn't paywalled:
"Evolutionary Origins of Your Right and Left Brain"
https://www.scientificamerican.com/arti ... eft-brain/
Jonathan
PS: Those of an inquiring mind may be wondering at this point how coded genetic information can ever generate asymmetry. Either for the brain or for the heart and associated plumbing...