No direct experience here, but I know there is Vulkano[1], a Rust library that wraps around the Vulkan API. But until (and if) a SPIR-V target is available to the Rust compiler, the compute shaders will still have to be programmed in another language (typically, GLSL). This covers the GPU side of your interest.
I don’t know how things stand in the embedded Rust camp, however.