Okay, so after looking through the posted system information, I found that it detected an old icd placed in /etc/vulkan/icd.d/ stating the api version was only 1.0.3.
Apparently when launching games through proton, it chose this icd by default and not a more up-to-date one placed elsewhere. I guess this made DXVK think only Vulkan 1.0.3 was supported and thus crashed.
Deleting this directory, as icds are now saved under /usr/share/vulkan/icd.d/ instead, fixed the issue. This was never a problem with DXVK. Sorry for noise
After Valve released Proton 5.0, every game that have made use of DXVK started crashing on launch, so I naturally opened an issue there: https://github.com/ValveSoftware/Proton/issues/3573
Debugging the issue eventually led to bisecting DXVK, as release v1.5.1 worked fine, but release v1.5.4 had problems. Through bisection, I found https://github.com/doitsujin/dxvk/commit/252ec9406d864e64949ec60ab20fe24e1dbc6262 to be the first bad commit. After checking out the master branch again and reverting said commit, games would start launching again. I guess this also explains why the wine would crash right as the supported Vulkan properties is being written to the log, as can be seen in the attachment on that issue.
Another user on the mentioned issue also seems to have the same problem, and he's also using an RX 580 GPU, but a newer driver. Perhaps it's some quirk with RadV and that specific GPU not properly supporting this Vulkan extension? In which case, it would be a bug with RadV and not DXVK.
Running Vulkan Info, I also see VK_KHR_get_physical_device_properties2 among the instance extensions, but that's the only occurrence of get_physical_device_properties when using grep on the output.
System information