Hi fajja,
It sounds like you have been unable to startup your Mac since you've updated to Big Sur. You mentioned that you're seeing errors when you go to startup your Mac.
To begin, take a look and see if any of these screens match what your'e seeing when you try to startup your Mac since installing Big Sur: If your Mac doesn't start up all the way.
If none of the screens match what you're seeing, try restarting in safe mode and test again: How to use safe mode on your Mac.
Do you know if your Mac was backed up before you started the update? You can find out more information about how to back up your Mac here: Back up your Mac
Let us know the results and the additional information if the issue persists.
Cheers!