Vulkan is an experimental and unstable API, things like this happening are understandable. Perhaps your on-board supports a higher version of Vulkan than the GPU, so that’s why it’s preferred by Xenia?
Ordinarily, the solution would be to tell the emulator to use the more venerable OpenGL, but the case with Xenia is that it’s an experimental emulator running inside of a Wine container translated using the experimental vk patch. ie. you need specific hardware to get it working in the first place, and even then there are a lot of commercial games not functional yet with Xenia using Vulkan (compared to DirectX natively on Windows). The reason there are no options for Xenia like that yet are that there are no available options.
It would be surprising to see this working at any playable speed on a laptop of all things. But for now, the only thing an end-user could do is wait. Wait for Xenia to develop a bit more as an application, wait for more hardware to support more versions of APIs.