You're getting a lot of answers that blatantly contradict the canon.
Two stormtroopers pick up the lifeless body
A pair of white-armored stormtroopers lifted Captain Needa’s lifeless form
Stormtroopers swoop in to dispose of Captain Needa’s body.
The air stops flowing to his lungs. Blood ceases circulating in his brain. His eyesight fades to white
But let's consider the canon. The canon is what was fixed forever in celluloid in 1980. And that canon tells a different story.
Firstly, Needa doesn't suffocate to death. Suffocating takes four or five minutes of oxygen deprivation and that deprivation must continue after the point of unconsciousness for a considerable time. Even blocked circulation to the head won't kill a person in just seconds. A crushed windpipe would leave a man struggling on the floor for minutes as the life drained out of him while his lungs struggled to draw enough oxygen.
If Vader killed him with force choking, it would have to have been by breaking open his carotid arteries or rather implausibly by snapping his spinal column. No evidence of massive internal bleeding is obvious on screen as major artery breech would quickly reveal, but we can't rule it out completely.
So all the sources that emphasize difficult breathing, fading to white, and wheezing to death are not to be taken seriously. They contradict what we saw on screen. They directly rewrite the clear and definitive canon of Empire.
Let's also consider the idea that stormtroopers dragged Needa away. White armored stormtroopers is certainly a memorable image that might be conjured up by someone familiar with the Empire but totally ignorant of Needa and Vader's interaction. In fact, it was black-clad Imperial Marines that picked Needa up.
That should tell you all you need to know about the credibility of those non-canon sources.
In canon, we simply don't know if Vader killed Needa. It's likely that Vader and Needa themselves didn't know until a thorough examination of Needa's neck injuries by the Imperial Navy Medical Corps could be completed.
So let's remember that a lot of people, some of them writing for Disney and Lucasfilm, write a lot of things. None of them are Star Wars canon unless they're fixed in celluloid. Novelizations and preliminary script leaks are the galaxy's fake news. Don't be taken in.