That is in fact not what the Supreme Court said. It said that the President has immunity for “official acts,” just like Congress members and judges.
Say a judge dismisses an indictment of an accused murderer because the police didn’t have a proper search warrant. Then the accused murderer kills someone else. That could fall within the letter of “negligent homicide” laws, but the judge can’t be prosecuted for that because judges have absolute immunity for official acts.
Similarly, a red state prosecutor could have tried to prosecute Biden for something like negligent homicide on the theory that his opening of the boarder was a negligent act that resulted in deaths. Obviously you can’t do that, because the President has immunity for official acts. It would be completely insane if the President didn’t have immunity. President do lots of things which cause people to be killed, property to be destroyed, etc. You could prosecute those as crimes if you literally applied the criminal laws.