You have signed out Apple ID from Mac system preferences , click on ok in your Mac as shown in your screen shot .
Few questions -
( a ) Do you have correct answers for security questions , date of birth , rescue mail address and its password .
( b ) The correct Apple ID and its password .
Its seems system preferences is not responding , run safe mode and again try to sign in with correct credentials while working in safe mode Mac startup key combinations - Apple Support
Note : don't post any Apple ID account credentials here , you might be using any vpn services , unknown softwares / apps / anti virus , in case if they are installed from finder > applications , right click on them and move to trash , restart and empty the trash .
In later stages you have to convert secondary authentication into 2FA ( as Mac OS catalina 10.15.7 ) is used .
Read Method to sign out from iCloud account . - Apple Community