Games like First Session
Games like First Session include Mouthwashing, No, I'm not a Human, SOMA, Still Wakes the Deep, and Layers of Fear (2016). We matched them by the tags players give First Session on Steam (Psychological Horror, Horror, Story Rich, Atmospheric, and Retro): closest matches first, and among equally close ones the better-known games.

Mouthwashing
Shared: Psychological Horror · Horror · Story Rich

No, I'm not a Human
Shared: Psychological Horror · Horror · Story Rich

SOMA
Shared: Psychological Horror · Horror · Story Rich

Still Wakes the Deep
Shared: Psychological Horror · Horror · Story Rich

Layers of Fear (2016)
Shared: Psychological Horror · Horror · Atmospheric

Fran Bow
Shared: Psychological Horror · Story Rich · Horror

Outlast
Shared: Horror · Psychological Horror · Atmospheric

MiSide
Shared: Psychological Horror · Story Rich · Horror

Sally Face - Episode One
Shared: Psychological Horror · Story Rich · Horror

What Remains of Edith Finch
Shared: Story Rich · Atmospheric · Walking Simulator

Detention
Shared: Horror · Psychological Horror · Atmospheric

Firewatch
Shared: Story Rich · Atmospheric · Walking Simulator

Outlast 2
Shared: Psychological Horror · Horror · Gore

Fears to Fathom - Norwood Hitchhike
Shared: Psychological Horror · Horror · Atmospheric

Hellblade: Senua's Sacrifice
Shared: Atmospheric · Story Rich · Psychological

FAITH: The Unholy Trinity
Shared: Horror · Psychological Horror · Story Rich

Amnesia: The Dark Descent
Shared: Horror · Psychological Horror · Atmospheric

SILENT HILL 2
Shared: Psychological Horror · Horror · Story Rich

Amnesia: A Machine For Pigs
Shared: Horror · Story Rich · Psychological Horror

Little Nightmares II
Shared: Horror · Psychological Horror · Atmospheric

Little Nightmares
Shared: Horror · Atmospheric · Story Rich

Tiny Bunny
Shared: Horror · Story Rich · Psychological Horror

Layers of Fear 2 (2019)
Shared: Psychological Horror · Horror · Atmospheric

The Beginner's Guide
Shared: Story Rich · Atmospheric · Indie