My laptop upgraded to Big Sur but now, my Safari is not working, what is the matter?

Boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and see if the problem persists. Reboot normally and check again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

Have you installed or run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac?

you can start with these two apple support articles:

If you can’t open a website in Safari on Mac - Apple Support

Safari troubleshooting on Mac - Apple Support

Your screenshot indicates that you have lost your internet access. Have you checked it? Are you able to send and receive emails? Do you have other access to the internet with a different browser? Maybe you need to reenter the password to reconnect to your router. Maybe it needs to be reset.

My standard practice with internet connection problems is to first turn of the router for 10 seconds. After turning back on the router will boot up and hopefully reestablish a connection with your machine.

After upgrading to Big Sur - did you Migrate anything from an older version of macOS