I am quite sure PS5 doesn't do Vulkan at all, and you even don't need a NDA access for that, there are enough GDC talks and SCEE presentations on the what APIs Playstations do support.
It’s not clear to me that the PS5 supports Vulkan at all (excluding third party translation layers). I would be happy to see any evidence. In any case I’m confident the large majority of PS5 games use its native api GNM.
GNM could certainly be implemented for Intel GPUs, but it’s an additional cost to account for.
So I’m not buying that going Intel would lose backwards compatibility.