Mac OS update has an invalid signature
It sounds like it could be a corrupt plist file or something else entirely. You didn't happen to remove any certificates from Keychain did you (accidentally)? Apple uses those for verifying code signatures.

One simple idea to try is to create a new admin account on your computer. Login and see if you're able to update the OS from that account. You can delete that account after the system if updated, or at least, you've now isolated the problem to a single account.

If that fails, I might try just re-installing macOS from the recovery partition. This will overwrite the system files but shouldn't affect anything else.