Your system info says that you have a intel HD graphics, and that CPU has the 4th generation that I had too. There is no support of vulkan in windows because there are no official drivers for this GPU to run, at least from intel. In fact it doesn't support even DirectX12. It is capable of running vulkan, but I know only in linux. It has some drivers that works with it, but support is limited: the GPU is capable of running the latest 1.3 vulkan, but performance is comparable if not worse to OpenGL.
Do skinning work with OpenGL 4.3 though?