The player instance is not saved.
Let's say you nested each level more or less like this:
main node for the level > assets like tilsets, etc + an instance of player node
whenever the scene is loaded, it loads that tree, and when it's changed that tree is deleted in favor of the new scene you changed into, and this new scene will load everything from their own tree of nodes.
In shot, player is not kept on RAM in-between levels/scenes, so you don't have to worry about it.