Murdering political rivals isn't a core constitutional duty of the President with automatic immunity. If he orders Seal Team 6 to do it, it's an official act, for which he has a rebuttable presumption of immunity. That means the prosecution has to prove he hasn't got immunity.

Roberts at least strongly hints in the majority opinion that Trump's immunity for trying to coerce Pence to commit crimes on Jan. 6 should be rebuttable. If that's the bar then ordering Seal Team Six to kill people will definitely get a president sent to prison the day he leaves office, whether the regular way or by impeachment.

Immunity before impeachment has pretty much been the position of the Justice Department (I think wrongly btw) with regard to current presidents for decades, including the Biden justice department. This isn't as big of a change as it makes sense for the Democrats to make it out to be.