I feel a bit uncertain about the use of tense in the above sentence structure.
Which one is grammatically correct and sounds most natural between "what it did was," "what it did is," and "what it does is"?
"What it did is" has a tense conflict. Since "did" is past tense, it is jarring to use "is" in present tense. "What it did was" is perfectly fine when indicating what something did during a specific event in the past.
"What it does is", on the other hand, doesn't indicate you're describing a specific past event. It indicates that you're either telling us what it is doing now, what it does in general when called upon to do something, or what it would do in a particular situation.