Games like Washout
Games like Washout include Outlast, Mouthwashing, Layers of Fear (2016), Phasmophobia, and SOMA. We matched them by the tags players give Washout on Steam (First-Person, Surreal, Casual, Supernatural, and Psychological Horror): closest matches first, and among equally close ones the better-known games.

Outlast
Shared: First-Person · Horror · Psychological Horror

Mouthwashing
Shared: Psychological Horror · Horror · Atmospheric

Layers of Fear (2016)
Shared: First-Person · Psychological Horror · Horror

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

SOMA
Shared: Psychological Horror · Horror · Atmospheric

Lethal Company
Shared: First-Person · Horror · Psychological Horror

Pacify
Shared: Horror · First-Person · Psychological Horror

Visage
Shared: Psychological Horror · First-Person · Horror

Poppy Playtime
Shared: First-Person · Horror · Psychological Horror

Outlast 2
Shared: First-Person · Psychological Horror · Horror

Still Wakes the Deep
Shared: First-Person · Psychological Horror · Horror

Five Nights at Freddy's
Shared: Horror · Psychological Horror · First-Person

The Mortuary Assistant
Shared: Supernatural · Horror · Surreal

Firewatch
Shared: First-Person · Atmospheric · Walking Simulator

Garten of Banban
Shared: First-Person · Horror · Psychological Horror

DON'T SCREAM
Shared: First-Person · Psychological Horror · Horror

No, I'm not a Human
Shared: Psychological Horror · Horror · First-Person

What Remains of Edith Finch
Shared: First-Person · Atmospheric · Walking Simulator

Fears to Fathom - Woodbury Getaway
Shared: First-Person · Psychological Horror · Casual

Amnesia: A Machine For Pigs
Shared: First-Person · Horror · Psychological Horror

POOLS
Shared: Psychological Horror · First-Person · Surreal

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

Ghostwire: Tokyo
Shared: First-Person · Supernatural · Horror

[Chillas Art] The Convenience Store
Shared: Horror · Psychological Horror · Casual