I got my first crash during the video sequence on the mind flayer ship. After this I get a crash randomly whenever I am saving, usually on the second to third try, it seemingly does not matter if it is auto, quick or regular.
What I have found is that savegame files seem to go missing after a crash, at least if they are made shortly before the one where your game crashes, which seems odd.
I can not tie these crashes to any kind of event or anything, really don't see any connection there so far.

Trying to run the game with Vulkan/Dx11 does not change anything as far as I can tell, running as admin doesn't do anything either.
I did a manual install of Vulkan drivers but instead of fixing something I got a crash just by changing things in the options menu. Switching between Vulkan/DirectX does fix the issue until the next time it's saving.

That is all I found so far.