Allow me to disabuse you of the notion presidential immunity is part of the Constitution. It's a construct entirely of the conservatives on the courts making.
Its not spelled out in the Constitution, but the courts have always upheld it.
See Sovereign Immunity reference below. The USSC interprets the LAW, duh.
Under Presidential Immunity from Wiki
The
Constitution of the United States grants
legislative immunity to members of
Congress through the
Speech or Debate Clause, but has no explicit comparable grant for the president. Early American politicians, including those at the
Constitutional Convention, were divided as to whether such immunity should exist. However, courts historically found that the president had absolute immunity from any personal damage liability for acts undertaken in the course of his duties. The first suit brought directly against a president was
Mississippi v. Johnson (1867), in which the
Supreme Court of the United States ruled
Andrew Johnson could not be sued as the actions in question were discretionary.
Spalding v. Vilas (1896) affirmed that federal
cabinet officers had absolute immunity for actions "more or less" within the scope of their duties;
Barr v. Matteo (1959) extended this to all federal executive officials.
en.wikipedia.org
Absolute immunity applies to acts that, if subject to challenge, would significantly affect the operation of government, such as would occur if a legislator could be sued for core legislative acts, and is also typically extended to statements made on the floor of the legislature. Similar protections apply to judges who are acting in a judicial capacity