390xx driver has no vulkan support. 470xx supports it. Probably not detected correctly. According to this site: Appendix A. Supported NVIDIA GPU Products your card should be supported by up to 470xx, but not 560xx. Compare the chip ID (Device PCI ID).
So try:
sudo mhwd --remove pci video-hybrid-intel-nvidia-390xx-bumblebee
# and then
sudo mhwd --install pci video-hybrid-intel-nvidia-470xx-prime
Also note, that the newest DXVK (DX8-11) and VKD3D (DX12) needs at least Vulkan support for v1.3 and I guess 470xx supports only up to v1.2. So try an older proton version. 
This is usually done to control the dGPU:
prime-run vulkaninfo
prime-run vkcube