Sovereign Immunity does not extend to illegal acts.
And the supreme court has already ruled that a sitting president can be sued.
Yep.
And the Constitution provides for impeachment and removal of a president or any other federal official. The people and state governments are the actual sovereigns, so they get the final say.
The Founders did recognize the President as Head of State, and so endowed the office with enough of the customary sovereign powers so that a president would have to be taken seriously, at home and abroad.