Is there something like a node ID which is specific to that node and will be the same no matter how often I execute the game? That would be super useful for saving and loading games.
What is your use case? That would help narrow down a good solution.
Node path could likely work. You could also add a uuid or similar (there's an extension that provides a uuid implementation).
Might be hacky, but you could tap into this and see if it suits your needs
https://docs.godotengine.org/en/stable/classes/class_resourceuid.html