Slightly OT: I never heard of webGPU before. So, in theory it will be feasible in a few years to run models like Stable Diffusion on my GPU through the browser without fighting with conda, pip and drivers? Or did I get the scope of this wrong?
WebGPU will not expose Nvidia-specific tensor cores, at least initially. But the main issues are with loading and processing gigabytes of data in browsers, which aren't addressed by WebGPU at all. You'll have difficulty downloading and storing all that data and quickly run into out of memory crashes.
The biggest issue I see is that those models (or rather their trained parameters) are usually pretty large (several GiB). So it'll take a while to set up in the browser before the evaluation can actually start. It'll also require a lot of bandwidth on both ends.
A lot of those things should already be doable with the fragment shaders we get from WebGL and a lot of hackery, like clever (ab)use of textures. So the actual issue that we're not seeing a lot of this is probably not due to it being impossible right now...
Might not be feasible due to memory constraints (I'm not sure), but browsers can load data from disk into memory without having to touch the network. So you could in theory ask the users to download the model separately, then ask them to select it from a file picker, and the browser can have access to it that way.
As far as I understand, the approach allows far more flexibility, at the expense of higher complexity. It's less "stateful" than WebGL, which basically gives you a big class that manages everything OOP-style.
Apple does support WebGL2, but compute shader support is not part of that core spec. The demos[2] certainly don't work in Safari in my quick test.
[1]: https://registry.khronos.org/webgl/specs/latest/2.0-compute/
[2]: https://9ballsyndrome.github.io/WebGL_Compute_shader/webgl-c...
There are still notable gaps, like no bindless resources or raytracing though. So don't expect e.g. unreal engine to run on WebGPU without some significant compromises.