Afaik the way it works in Vulkan is that all the string formatting is actually done on the CPU. The GPU writes only writes the data to buffers with structs based on the format string.

All the shader prints are captured by tools such as Renderdoc, so you can easily find the vertex or pixel that printed something and then replay the shader execution in a debugger.

I only wish that we would've had this 20 years ago, it would have saved me so much time, effort and frustration.