Parallax is done using a separate layer node for each portion of the background. The "scale" attribute is used to set how much each layer moves in relation to the player. You can check out the "level_template.tscn" file in the source code to see how it was done here.
Pretty clear code in your project compared to my entry! Turns out I did the same for parallax, but with me it did not work. Perhaps because of a different version of godot?
