I'm not a Superman aficianado, I just watch the films and used to read comics in the 70's-90's.
Has there ever been a version of Superman where his powers are explained as Kryptonian super-science tinkering with their own biology?
No. Least not in the normal comics. Theres been alot of "What If" versions in Elseworlds where his powers originated from other sources.
Doomsday on the other hand is exactly this. A genetically engineered creature forced to survive on the most deadly planet ever. Primordial Krypton and possessing all the powers of a kryptonian and more.
Theres also been paralell universes where their version of Superman was something else. Ultra Man from the Crime Syndicate for example.
But...
There is the Tangents Superman who IS genetically engineered. This one is a black detective named Harvey Dent. His power though is that his brain and intellect are constantly evolving and improving. Giving him eventually vast mental powers.
The Tangent univers was a pretty fun twist on everything DC.
The Flash was a girl who had light based powers. Wonder Woman was an alien who could think things out of existence. The Joker was a female vigilante. Batman was a knight who saved King Arthur but cursed to be trapped in Castle Bat until he can perform enough good deeds via an animated suit of armour. The Aquaman was a villain, a scientist turned into water and inhabiting the ocean, plotting to destroy the moon as the tides prevented him from gaining full power. and so on.