[What would happen if another country openly attacked Biden or any POTUS and killed them]
Yes, the U.S. response would be nearly-automatic there as well. Straight to Defcon 2 or Defcon 1 and pieces start moving.
I recently read a book titled Raven Rock written by Garrett Graff, it goes thru the US Nuclear Preparations since Hiroshima and Nagasaki, everything from who becomes POTUS in the event the POTUS, VPOTUS and others all get taken out at one time, how to pass the nuclear command to that person, fallout shelters for the Congress, etc.
Scenarios were planned out like what would happen if the POTUS was taken out and the VP was in another part of the world, who would have the nuclear football and were they in a position to take command, it’s fascinating and given the times we live needs to be considered.