Does this happen to be a 2018-2020 Mac with a T2 security chip? I think you just encountered one of the annoying bugs with the T2 chip.....losing the ability to authentic properly.
Can you still boot & successfully log into macOS?
Do you still have a macOS user account which still shows as being an "Administrator"? Check the "Users & Groups" System Preferences/Settings to be sure you have at least one active admin user account available.
If you still have a macOS admin account, then you may need to try a DFU firmware Revive to reset the T2 security chip to see if that makes any difference.
Maybe you can try reinstalling macOS over top of itself (not sure if that is possible by running the macOS installer while booted into the OS which you are trying to update). Otherwise create a new APFS volume and install macOS to the new APFS volume assuming you have at least 80GB+ of Free storage space (ignore the "Available" value since it is very misleading). The idea here is to get the T2 security chip to refresh itself so it can recognize an macOS admin user account that you can use to successfully authenticate with when booting into Recovery Mode.
If you previously modified the security settings to allow booting from USB, then you could create & use a bootable macOS USB installer instead to reinstall macOS over top of itself.
Edit: If you can still boot into macOS, then before doing anything else......make sure you have a good backup while you still can because you may not get another chance. If macOS stops booting, then you will have no way of accessing the data on the internal SSD if you cannot authenticate with the T2 security chip.