I experienced the same issue with my MacBook Pro (2017) just this morning.
In sincere hopes that this advice may help someone...
This is what happened in my case:
My Norton 360 anti-virus software was misbehaving (the Norton dashboard would not open when I start it).
Since my annual subscription was close to an end, I ordered the renewal and decided to delete current installation and install newest version fresh from new download.
I force deleted the installation of Norton by moving it to Trash (bad idea).
As soon as I finished force delete, Norton dialogue box somehow popped up and asked me to restart in order to complete the uninstall. This appeared strange because I already deleted the software in previous step. (Obviously, there were remnants of Norton still lingering around my MBP. Hint: uninstalling Norton is very difficult...)
After the restart, I started getting the same "Critical software update required" loop error message, and that's how I ended up on this discussion portal. I've tried most of the troubleshooting tactics offered here (3min waiting game, wired ethernet connection, I also considered upgrading to Monterey but didn't), but nothing worked in my case.
Here is what worked though:
Restart in Safe Mode (hold left Shift + Power button)
Re-install and activate Norton
Restart MBP to complete Norton installation.
My MBP is now fully functional, and the first step that I am planning on doing is take a backup of all my work (music tracks, video edits) to my external hard disk before something else bad happens...
In my case, the issue seems to have been caused by forced Norton uninstall and simple reinstall brought my MBP back to life. So, if this issue happens to you, consider what you have done to your MBP just prior to this error message. You may be able to unwind it...