AMD’s RADV doesn’t do the common compute APIs

RADV is just the Vulkan driver to be clear, so the other APIs are implemented separately. ROCm is supported by some cards, and Rusticl is the currently most advanced OpenCL implementation in Mesa (with Clover on the way out). Vulkan compute is implemented in RADV, although I found it to be slightly slower than the AMDVLK implementation (AMD's official Linux Vulkan driver, developed out of tree).

As for Nvidia, it's likely to be a worse situation since Nvidia don't have a bunch of open APIs, just closed ones. Vulkan compute I would expect at least, if not immediately.

As for CUDA, it might work if you're willing to have a hybrid open/closed system. On AMD this is possible, where you can generally install and enable/disable the AMDGPU-PRO compute and Vulkan drivers on demand.