DirectX 11 is sometimes your only choice if you want to play splitscreen couch co-op on the PC.
Vulkan results in many graphical glitches and certain areas are unrenderable (the culprit being the black boxes so many people mention). My partner and I reached a point where we couldn’t move on anymore and graphics drivers were already updated and game was already updated so we were confused as how to move forward.
After searching for a few hours, I found a post specifically about the splitscreen and how this seems to affect lots of people trying to play splitscreen with Vulkan.
I personally prefer Vulkan and think it runs better in single player mode, but if you want to play splitscreen without major issues, I strongly suggest DirectX 11.