dkms – Cannot modprobe wireguard on Ubuntu 20.04

I cannot make wireguard work on my Ubuntu 20.04. I think my main issue is that the wireguard module is not loaded. When I do modprobe wireguard I get:

modprobe: FATAL: Module wireguard not found in directory /lib/modules/5.4.0

The error message makes sense, since the wireguard module has been built to /lib/modules/5.4.0-77-generic/updates/dkms/wireguard.ko

$ find / -iname "*wireguard.ko*"

I am also confused by the following error message when I execute lsmod | grep wireguard and I’m not sure if it is related to wireguard:

libkmod: ERROR ../libkmod/libkmod-module.c:1941 kmod_module_get_holders: could not open '/sys/module/crct10dif_pclmul/holders': No such file or directory

What can I do to load the wireguard module?

Here is some further information that could be relevant:

$ lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 20.04.2 LTS
Release:        20.04
Codename:       focal

$ uname -a
Linux mysecrethostname 5.4.0 #1 SMP Mon Dec 9 19:36:21 MSK 2019 x86_64 x86_64 x86_64 GNU/Linux

Installed linux-headers packages: linux-headers-5.4.0-77, linux-headers-5.4.0-77-generic, linux-headers-generic

Wireguard versions:

wireguard 1.0.20200513-1~20.04.2
wireguard-dkms 1.0.20201112-1~20.04.1
wireguard-tools 1.0.20200513-1~20.04.2

Module build log:

-------- Uninstall Beginning --------
Module:  wireguard
Version: 1.0.20201112
Kernel:  5.4.0-77-generic (x86_64)

Status: Before uninstall, this module version was ACTIVE on this kernel.

 - Uninstallation
   - Deleting from: /lib/modules/5.4.0-77-generic/updates/dkms/
 - Original module
   - No original module was found for this module on this kernel.
   - Use the dkms install command to reinstall any previous module version.


DKMS: uninstall completed.

Deleting module version: 1.0.20201112
completely from the DKMS tree.
Loading new wireguard-1.0.20201112 DKMS files...
It is likely that 5.4.0 belongs to a chroot's host
Building for 5.4.0 and 5.4.0-77-generic
Module build for kernel 5.4.0 was skipped since the
kernel headers for this kernel does not seem to be installed.
Building initial module for 5.4.0-77-generic


Running module version sanity check.
 - Original module
   - No original module exists within this kernel
 - Installation
   - Installing to /lib/modules/5.4.0-77-generic/updates/dkms/


DKMS: install completed.