We did some further investigating and wanted to give an update:
Unreal 5.2 still works without any crashes, so the problem with the Vulkan crash seems to have started with UE5.3. We could not identify the reason for the crash so far.
Unreal 5.2 is not without issues though. It works when packaging for Windows, both with DX12 and Vulkan. However, when packaging for Linux the package runs but there is an issue with the skylight that only appears on Linux (with and without ndisplay). The skylight, or at least the shadows, are black, at least when lighting is not precomputed.
Unfortunately that makes UE5.2 not usable for us as well.
Any advice - either with the UE 5.3 Vulkan crash or the UE 5.2 skylight issue - would be very much appreciated!