I have now been troubleshooting this problem on a MacBook for over 2 hours.
Macbook Pro Retina 2015 model upgraded from Mojave to Big Sur. System then had a Migration Assistant run performed to restore from another computer's Big Sur backup.
The Admin account from the previous computer was added as an admin during the migration (Admin2). The Admin account created during the Mojave installation process was preserved for now as well (Admin1)
After this, attempts were made to change settings in the Security & Privacy menu.
- SMC reset has been attempted at least 3 times. Since this is a 2015 non-T2 system, SMC reset was performed with left (Shift/Ctrl/Option) keys and holding power for 10+ seconds.
- Admin1 was unable to unlock the S&P menu.
- Admin2 was unable to unlock the S&P menu.
- Admin1 and Admin2 can unlock the Users & Groups menu.
- Admin1 and Admin2 can create a new admin user via the Users & Groups menu (Admin3).
- Admin3 was unable to unlock the S&P menu.
- Admin1 and Admin2 can run sudo su in terminal successfully.
- Admin1 and Admin2 can manually create a new user and assign that user admin rights via terminal commands (Admin4)
- Admin4 was unable to unlock the S&P menu.
- The system was rebooted to recovery mode and .AppleSetupDone file is deleted
- New Admin user is created during OS X Initial Setup process (Admin5)
- Admin5 was unable to unlock the S&P menu.
- The system was rebooted to recovery mode and resetpassword (Authenticated via Admin2) for Admin1
- Admin1 was unable to unlock the S&P menu.
Clearly, admin access is not a problem anywhere else but the Security & Privacy panel. At this point, I'm convinced the problem is some sort of issue with the System Integrity Protection settings for the S&P panel during the transition from Mojave to Big Sur.
Reports from some people that upgrading from Big Sur 11.1 to 11.2 back when this initially came out makes me think that the SIP settings are being fixed during the update process, per "When you update Apple apps or upgrade macOS, the installer will check and reset the permissions of any item if necessary." But since I upgraded this computer from Mojave directly to Big Sur 11.4, there's no way for me to manually fix those settings that I'm aware of.
For anyone upgrading to Big Sur, it may be advantageous to obtain the installer for the version previous to current, then run the update to the next version to possibly avoid this headache altogether.
In the mean time, I guess it's time to Time Machine and wipe this machine, install Big Sur from scratch, and see if things work better after that.