>Would it? I am skeptical about this take and I am skeptical of Sotomayer’s take. What official capacity would Nixon have been undertaking?
For the Nixon tapes, today's SCOTUS ruling would require the prosecution to convince a federal judge before trial that the value of the tapes in the criminal case greatly outweighs the general immunity from oversight presidents have when consulting advisors. Difficult, but not impossible. It probably would've given the same result in the Nixon case, because Nixon didn't use presidential powers to carry out the plan (just the cover up in the Saturday Night Massacre stage). If he had used an active FBI agent instead of a former one to place the bugs, then it might have been OK, according to today's ruling (see III.B.1 which grants immunity to Trump for his sham investigations using the DOJ).
>What official capacity would a seal team six assassination of trump be designated as?
The President is the head of the military and can direct them without consulting Congress. Congress is free to impeach him if he does so without authorization, but he'd have absolute immunity because this is a core power of the office.
Maybe you meant, "What reason could there be to justify that killing in the name of the nation or its people?" In which case, the President would never have to say. His motives are not even allowed to be investigated. See III.A from the majority opinion:
>In dividing official from unofficial conduct, courts may
not inquire into the President’s motives. Such an inquiry
would risk exposing even the most obvious instances of of-
ficial conduct to judicial examination on the mere allegation
of improper purpose, thereby intruding on the Article II in-
terests that immunity seeks to protect.