Chrome officially supports WebGPU on all platforms except Linux for now, you can force it on with a flag but it's obviously not meant for prime time yet. Firefox has yet to officially ship WebGPU at all but it's supposed to be coming in version 141, due at the end of July. Safari is still dragging its feet with no indication at all of when they'll get around to shipping.
Is there some reason WebGPU has difficulties getting implemented for Linux, like DRM features or so?
WebGL is that, but for OpenGL ES 2.0, and WebGL 2 is that but for OpenGL ES 3.0. WebGL is OK for graphics, but pretty hard to effectively adapt for compute / simulations.
WebGL has a bunch of limitations, but a big one is that you can only use the gpu to move around triangles vertices (vertex shader) and color them in (pixel shader).
If you want to do something like that cool water simulation you have to do some painful hackery to pretend all your data is actually vertices or colors in a texture. Even with hackery, there's still lots of things you simply can't do.
WebGPU supports compute shaders which let you read and write whatever data you want.