Hi all,
I have the same problem, Mac mini (2020) (Intel) with an external monitor, as others, either from the normal login or using Recovery Mode, it either locks up (typically "10 minutes to go") or just fails.
I tried Safe Mode, it looked much as if it was going well, but then the Screen Saver kicked in, and I couldn't enter a password to get out of it!
So I tried again,
Start in Safe Mode
Disable Screen Saver (the monitor powers down after a while by itself, but that's not an issue, if the screen updates or any keyboard key is pressed it comes back to life)
Change wallpaper to a fixed wallpaper (disable "Change Picture")
Then kick of the update of "Big Sur" to v 11.1 (from v 11.0.1)
It just did everything as required, rebooted, came up in "normal' mode I logged in and all done!
I am not sure how much the screen saver messed things up (in conjunction with Safe Mode) , but it certainly seems to have made difference, the wallpaper being fixed is just one less thing to be going on at update time (probably not needed)!
Anyway, this worked for me (having tried some of the other offered solutions first)...
Hope it helps somebody else
Cheers Derek-b