Thank you!
The physics is mostly standard Godot engine physics. The characters are RigidBody2Ds held together with Pinjoints. That makes stuff like the ragdoll function easy, because all you have to do is turn off the Pinjoints. Getting the mouse to pull the character required some custom force integration, but it wasn't really any more complicated than defining a force from the hand position to the mouse position.
Good luck with your own coding!