Galla
I can already see from your code you will have issues with also using analog inputs since you are not taking into account the Up and Down input. If I remember correctly, Ori allows you to use the analog stick to rotate or quickly snap to any direction you want without waiting for a full rotation to get to the desired direction.
This is a better way to make this work with both arrow buttons and analog stick:
##Remember to register your inputs in InputMap in project settings
var look_direction: Vector2 = Vector2(Input.get_axis("Left", "Right"), Input.get_axis("Up", "Down"))
var look_direction_length = look_direction.length_squared()
##Only record input when analog is pulled halfway
if look_direction_length > 0.5:
var input_look_angle = atan2(look_direction.y, look_direction.x)
head.set_rotation(input_look_angle)

The downside of this method is that you will no longer be able to rotate the arrow by pressing buttons, the arrow will instantly snap to the direction. You can find a way to mix both methods and see what works best for you.