On the other hand, international law only influences where the geopolitical setting allows it to. When it comes to the question of life and death for a superpower, international law no longer needs to mean anything.

I can observe an analogy of this for an individual person in a situation that he feels is life-threatening: criminal law or civil law are not the first things that come to mind but survival is. Only the one who first survives has a chance to return to law when things are settled back enough.

Only when backed by force. There is no higher power in the playground of states. Ultimately countries by themselves are not necessarily rational actors. Smaller states join larger power blocs (either coerced or voluntarily, essentially they are trading off sovereignty for protection) and their own individual freedom to act gets subsumed. When it comes to dealing with Great Powers, realism is about as good as we can get, it is also predictably one of the oldest schools of thought in political science. The LIO theory is great in the decade post Cold War, but the world is multipolar now.

To my understanding it doesn’t ignore international law so much as singlemindedly focus on the forces and interests that “truly” drive it and are inherent to nature, ie global anarchy navigated by power/security concerns.

“Anarchy is what states make of it” is a great search phrase to pull on this thread with to say the least.