Transhumanism doesn’t rise above the DNA programming but rather enhances the DNA programming. Transhumanism stems from our strongest drive to survive, that has been manipulated via our DNA. Transhumanism deals with preventing the aging process and maybe even preventing humankind from dying, but as long as it rises from our identification of being our physical body it is not beyond the DNA.
In spirituality we rise above the DNA programming by realizing we are not the physical body.
Transhumanism can be compared to owning a car, where we continually develop methods to protect the car from decaying. For example, by enhancing the oils we use, upgrading the motor and maybe even shifting the car from using gas to use pure energy!!! But at the end of the day if the driver, who has invested so much energy in bringing the car to its highest functional capacity, identifies himself with it, then he is still trapped in a limited reality.
Nevertheless, to say that the driver can invest in technology that will help the car to last forever without any mechanical problems, while understanding that the car is only a vehicle and not a reflection of himself, then this is spirituality.
So you can say that transhumanism is an evolution within the DNA, while spirituality is an evolution beyond the DNA.
Now this doesn’t mean that one cannot lead to the other. Maybe if transhumanism one day extends the human life span for thousands of years people will have a longer time to realize but on the other hand if transhumanism creates perfect bodies and minds maybe humanity will fall even deeper into the illusion that they are this body and mind.