If this is accurate, then why didn’t the SCOTUS simply say “No person is above the law. Period.”

Instead they said a president has immunity for official acts.

One of these statements is different than the other.

Because there are official acts that would be immune from generally applicable criminal laws. Murdering a political opponent isn't one of them. Not every potential crime can be characterized as an official act.

So if President Biden orders a cabinet official not to comply with a Congressional subpoena on the grounds that the material is covered by executive privilege, he's immune from a criminal charge when he leaves office that he obstructed a federal proceeding. That doesn't mean that he would equally be immune from criminal charges if he ordered an assassination of a political rival.

BTW, if immunity means someone is above the law, then the SCOTUS could never simply say "No person is above the law. Period." Because every member of Congress has criminal immunity for most of their official actions. If immunity creates a law-free zone making an officeholder above the law, then we've had that for several centuries now.