Can't use my 2016 year MacBook Pro due to a failed update. What are my options?

Yesterday morning I have turned on my 2016 year MacBook Pro (MacBookPro14,3) with touchbar, just to discover that it now shows the message that "A critical update must be installed to your Mac, yet the update cannot be installed, yet the Mac cannot be used till it will be installed", so what's now?

• I have retried multiple times as the dialog suggests.
• I booted into minimal mode by holding the left shift. It boots in this mode. In the App store I have, indeed, found a big update pending that "requires restart". I have updated all other apps but this was not helpful.
• I tried to reset the operating system by booting with CMD+R, this way of booting worked but no attempts to reset were successful.
• The Mac was running High Sierra. I have updated it to Big Sur from minimal mode, and even looks like I have succeeded. The error message now shows up in the differently looking dialog but it is still the same:

The message in App store about the important update that was visible under High Sierra is now gone. Under Big Sur, the updates tab is empty now.

Finder still shows over 500 Gb of free space remaining so this is not due simply running out of disk space. The diskutil list that remained accessible in safe mode shows the following output:

The Mac was bought in a normal store and worked flawlessly up to now. I have never opened it, never tried any major intrusions like disk partitioning and during the recent months in general was not doing anything serious with it. Apart from trashing the laptop, what are my other options now? Is the complete factory reset possible? Or would it run Linux maybe?

Apart from the advice how to fix the laptop, it would be very interesting to know what is the update here so critical that the computer cannot be used at all if it cannot be installed.

A quick Google search of the error message makes it seem common to Macs with a T1 chip (like yours), particularly its firmware. There isn't really a clear solution though. You could try:

• Internet recovery (Cmd+Opt+R at boot)
• A bootable installer.
• Disabling any firewalls through safe mode (Shift at boot), as they are said to cause issues by blocking an update from Apple
• Getting the logic board replaced

As for running Linux, depending on what point in the boot process the error occurs, it might be possible.