Boinc's Ubuntu installation instructions weren't much help, and LHC's blog post on the subject was... well, what's the antonym of helpful? Dumpster fire?
A VirtualBox upgrade is what finally fixed this error for me. Here's what I did.
First, make sure Boinc and all its processes are closed and then update your packages:
sudo apt update && sudo apt upgrade
Then import Oracle's public keys:
wget -q https://www.virtualbox.org/download/oracle_vbox_2016.asc -O- | sudo apt-key add -
wget -q https://www.virtualbox.org/download/oracle_vbox.asc -O- | sudo apt-key add -
Add the Oracle VirtualBox PPA
sudo add-apt-repository "deb http://download.virtualbox.org/virtualbox/debian bionic contrib"
Install VirtualBox 6.0 or newer:
sudo apt update && sudo apt install virtualbox-6.0
Lastly, start the Boinc Manager from your apps panel, and go to Tools > Event Log... and look for a line that says something like:
Wed 16 Feb 2022 11:38:05 AM CST | | VirtualBox version: 6.0.24r139119
If you see something like that, everything should be working. You can double check that virtualization is active on your LHC page. Just browse to your publicly listed computer info page, which should be something like:
https://lhcathome.cern.ch/lhcathome/show_host_detail.php?hostid=12345678
...where 12345678 is your Computer ID, which can be found by going to your Boinc Manager and clicking on LHC@home in your project list and selecting properties. When you go to your LHC computer info page, it should says something like:
Virtualization Virtualbox (6.0.24r139119) installed, CPU has hardware virtualization support and it is enabled
The solution was relatively simple, but it sure wasted a lot of time since there weren't any good instructions posted anywhere. If this saves you some time, please consider giving this solution or problem an up vote. Thank you, and happy crunching!