What API upgrade would GIMP need to be able process/render such realtime 2D/3D particle simulation:
No API change is needed. It is possible to write an plugin, that starts an extra window, that does 3D stuff and then pushes an image back to GIMP.
Of course a deeper integration would need more work.
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Could developers integrate Vulkan in GIMP to make this parametric particle simulation happen?
Escape Motions has some cool online tools that emulate fluid mechanics. Still really cool toys and not probably what you were looking for. 
Something like this. ANd create system to control number of particle sources etc as in Stardust.
https://juniorxsound.github.io/Particle-Curl-Noise/
Could developers integrate Vulkan in GIMP to make this parametric particle simulation happen?
Yes.