Has Stephen King written anything that either is or approaches the steampunk genre? Same question goes for diesel-punk and cyberpunk genres. I tried looking for something along those lines but didn't come across anything that stuck out.
No, Stephen King writes (or so far has written).
Straight horror, mostly set in "Small Town America".
Post apocalyptic horror.
Weird cowboy horror.
When he wanders off his well trodden "Small Town America" track he goes to other "Earths" in other dimensions, any computers or machinery encountered there are "artifacts" left by some Precursor rather than steam, diesel or cyber punk.
I can recall nothing that has the flavor of a any "x-punk" genre, or even indirectly references one.
by way of credentials: I have read (at least once) pretty much everything King wrote up to and including "Cell"
Beachworld was included in the collection Skeleton Crew. It is fairly straight science fiction. However the fact that the space ships are somewhat worn down, cyber augmentation is a thing, and the characters involved are freelancers, means it has a good case to be considered cyberpunk.
With the caveat that I have not read all of Stephen King's extensive oeuvre, I did a quick scan of it, searching for titles I had not read, and I believe the answer is no. While Stephen King has written science fiction, none of it would fall under what I would consider "cyberpunk", "dieselpunk", or "steampunk".