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I can recommend "Spiritfarer" under "emotionally impactful", too.

I think Cart Life was the first game that hit me this way (shortly before Papers, Please). It really made me empathize with the desperate situations the characters were in, and in a way that felt more fully realized than in Papers, Please, though that's also a great game.

'Gris' is also another game about mourning and loss, and is an absolute audiovisual experience on its own.

There is also "That Dragon, Cancer" but I haven't played it because emotional exhaustion is the last thing I want from a game.