First of all, **** Gojo matchups, they're worse than Goku vs Superman discussions.
Second of all, Darth Vader wins. **** your type 2 conceptual manipulation, here's why Vader wins.
The Force is described as an energy field created by all living things and existing throughout the entire galaxy, surrounds and penetrates all living beings as a naturally existing force, much like how air surrounds us despite being invisible to the naked eye. While the Force can function in some ways similar to Ki or other similar energy systems, in that it can be stored in the body as energy, its more fair to say that Force Users manipulate the existing Force energy in their surroundings and their bodies to achieve superhuman feats, rather than just manifesting it like a Ki blast or any other similar attack.
Why is this important? Because the Force surrounds Gojo as well, exists both around him and in his own body. It's also not similar to Cursed Energy, so Gojo can't reliably sense if Vader is using his abilities. But more importantly, the Force existence within Gojo means it can be manipulated from the inside, and can't be reliably blocked with Limitless like physical matter or Cursed Energy attacks.
With all this being said, Darth Vader can reliably kill Gojo with TK before Gojo can do the same.
Sure, there are some options Gojo has that can and could kill Vader, like Hollow Purple, Unlimited Void, and so on, but Vader's precognition means that Gojo is less guaranteed to land attacks before Vader can do the same, and Gojo doesn't tend to use his most powerful attacks unless he's backed into a corner. With Vader using an energy system that Gojo can't really detect, and Vader's TK options being more quicker and reliable, Gojo would end up taking the fight too lax due to Limitless until Vader pulls out the TK to kill Gojo, crushing his heart, head or neck before Gojo can realise Vader can bypass Limitless.
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