Following the ruling by SCOTUS in Trump v. United States (2024) that Presidents enjoy absolute immunity for their exclusive powers and presumptive immunity for their remaining official acts, I have seen it claimed by many that the president could kill people, e.g. assassinate a political rival using the forces at his disposal, and be immune to subsequent prosecution.

For example, this question was asked by Judge Sotomayor during the hearing of above case.

To me, the answer is quite obviously a resounding "no". Yes, the US president is the commander-in-chief, but his official duties are to lead the militia in its defense of the country. So, in order for an assassination to be considered an official act, it would need to be demonstrated that the act was done in reasonable adherence to said duty, which clearly would not be possible to demonstrate (in practice it would probably be the prosecution who would have to demonstrate the inverse, but that would be trivial.).

So why is Judge Sotomayor, and others, implying that this precedent allows the US president to kill people at will?