Arch Linux

I also met this problem.
It occurs between versions 1.2.203 and 1.3.204 of vulkan-icd-loader.
So I made bisecting test.
first bad commit: https://github.com/KhronosGroup/Vulkan-Loader/commit/232c6977d2017442dec6abe78fd62222f8d0a333
(part of: https://github.com/KhronosGroup/Vulkan-Loader/pull/779)

I went ahead and made the patch for vulkan-icd-loader-1.3.208 (helps on my local machine at least)

https://github.com/KhronosGroup/Vulkan-Loader/issues/894#issuecomment-1079267488

So, after some research, we managed to fully understand what the problem is.
As far as I understand, the problem is that libnvidia-fbc during initialization reports the minimum vulkan api 1.0.0, but after that it requests layers, which are supported starting only from vulkan api 1.1. And the issue only became known when vk-loader made some checks more precise (probably to properly match the vulkan api spec). Apparently there will be some more similar cases with the minimum apiVersion.
But a fix on the application side (driver in this case) would be more preferable, since more strict compliance with the requirements of the vulkan api specifications.

For now, the better solution is to increase the apiVersion that libnvidia-fbc tells vulkan on initialization.
In theory, changing to 1.1 should be safe since 510 versions of the driver should already support vulkan 1.3 (but for obvious reasons, only the nvidia developers can guarantee that this change alone is enough, besides, a similar situation may be in some other files)
This fix should be enough (I tested it on version 510.60.02, but libnvidia-fbc.so doesn't seem to change that often, so it might work on some previous versions as well.):
sudo sed -i 's/\xc7\x84\x24\xfc\x01\x00\x00\x00\x00\x40\x00/\xc7\x84\x24\xfc\x01\x00\x00\x00\x10\x40\x00/' "/usr/lib/libnvidia-fbc.so"

more info: https://github.com/KhronosGroup/Vulkan-Loader/issues/894

looks like some fixes for linux will be in 1.3.210 version, but the problem described above is related to nvidia-utils (or other packages with libnvidia-fbc.so file)

Fixed an issue where NvFBC was requesting Vulkan 1.0 while using Vulkan 1.1 core features. This caused NvFBC to fail to initialize with Vulkan loader versions 1.3.204 or newer.
https://www.nvidia.com/Download/driverResults.aspx/187526/en-us

fixed in 510.68.02