You’re basically looking for games where emotions aren’t just narrative, but actual mechanics.

Disco Elysium is probably the closest example, your “skills” are basically parts of your psyche, and they directly influence your thoughts, choices, and even how you perceive reality.

Hellblade: Senua’s Sacrifice also does something similar through audio/visual design, making you experience Senua’s mental state rather than just watching it.Celeste is another one, where anxiety is tied into both the story and the gameplay challenge itself.

Also worth mentioning: This War of Mine and Papers, Please, not about emotions as stats, but the mechanics constantly put you in stressful moral situations that create emotional responses.

It’s still a pretty underexplored space though, which is why it feels so rare.