What sort of things will compute shaders on the web unlock that wasn't possible before? Asking as someone with only a little graphics programming experience
They unlock a lot of advanced graphics techniques that are too slow to do CPU-side but work well in parallel on GPU. It's a pretty wide variety of things, but e.g. lighting, mesh manipulation, terrain, voxels, post-processing.
I think you'll begin to see more advanced particle systems and physical simulations for a start. And 3D Gaussian Splatting will probably benefit too (since compute will probably enable much faster sorting of splats). So it's not really that this stuff wasn't possible before...but compute will enable these techniques to run far faster.
With WebGPU, Stable Diffusion in the browser (watch out, once you click the "Generate" button, it will fetch 2 GByte of daaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaata) (and probably make your laptop hang whiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiile generating, as you can tell by my typing).