I think that the wireguard-linux-compat project doesn't officially drop CentOS 8 Stream support. The recent commit message just indicates that is no longer guaranteed to work, and it doesn't introduce any code changes that actually break the compatibility. The recent breakage is caused by a code change in kernel 4.18.0-394 instead. And that change could also be committed to RHEL8 eventually.
There is no proper instruction for C8S for now. The current workaround is do not update the kernel to 4.18.0-394. Or, if the kernel has been updated, try to build the wireguard module explicitly for the older kernel.