genuine question here, should this get the Self-insert tag? Because the doujin clearly stated that Yu here is used as a stand in for the "Anata" character in the game. And from what I remember, the character in game is not the same as Yu (different arcs and different personality).

I would argue that although "Anata" is the SIFAS protagonist, this isn't self-insert. It's clearly depicting her as a distinct character and not the kind of blank reader stand-in that a self-insert story has.