Awesome! I wanted to give you one tip: I noticed that you attached the background to the player, but in my time using Godot, I found it's best to put the background on the actual level. That way, when the player jumps, you won't see the base Godot background. It's just a tip, but other than that, your game is nice.
I noticed there was some odd behavior with the background I couldn't figure out. That was the first parallax bg I tried in Godot.
I actually made it it's own scene and when I added the scene to the level I added the sprite so I could use it for other levels but I don't think I set it up quite right.