I didn't get any hangs when I tried to add shader logging to the maximum GI shader to see what was going on, so that wasn't very helpful, and then I also got rid of the hang when I simply added a memory barrier after the second texel fetch. I've attached the modified shader that doesn't hang.
I can no longer reproduce this GPU hang with RX 3070 and 580.95.05. Old vkd3d-proton also works fine, so might be a driver or game bug that has since been fixed.
As reported here: https://github.com/ValveSoftware/Proton/issues/8221#issue-2638548329
It's a bit random with ultra settings, but on maximum GI it's pretty reliable, just idling in the main menu with the spinning globe for a minute or two should do it. The hangs happen in variants of the same shader named SCREEN_PROBE_MARCH_CS_Win64_SM65.
I also tried a shader override to see if it was a compiler issue, but I got the same hang that way.
Software information
Planet coaster 2, default settings, global illumination enabled.
System information
Log files
Breadcrumb traces and shader files: planet_coaster_2_logs_and_shaders.zip