Black Ops 6 is enforced through the current Call of Duty PC stack. Players describe the hardware ban the same way they do for Warzone: the machine is blocked, not only one profile.
A new account on the same PC is the clearest sign. If that account is refused at launch, the stored value is a hardware ID.
The Black Ops 6 spoofer is for that device record. It changes the identifiers the client reports from the computer.