with this code you are flipping the entire player, not only the sprite, meaning left and right get reversed, and all the rest of your player code will loose sense.
change it to to flip the sprite only
$NeoPlayer.scale.x = -1
$NeoPlayer.scale.x = 1
also, why did you created your own INPUT() function inside process, instead of using the _input(event) function that fires every time an input is received