Games like Papa
Games like Papa include Firewatch, Mouthwashing, What Remains of Edith Finch, Layers of Fear (2016), and Amnesia: A Machine For Pigs. We matched them by the tags players give Papa on Steam (Walking Simulator, First-Person, Horror, Psychological Horror, and Story Rich): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Walking Simulator · Adventure · Story Rich

Mouthwashing
Shared: Horror · Psychological Horror · Story Rich

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

Layers of Fear (2016)
Shared: Horror · Walking Simulator · Psychological Horror

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

MiSide
Shared: Psychological Horror · Horror · Story Rich

SOMA
Shared: Horror · Psychological Horror · Story Rich

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

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

Blair Witch
Shared: Horror · Psychological Horror · First-Person

The Beginner's Guide
Shared: Walking Simulator · Story Rich · First-Person

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

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

The Park®
Shared: Walking Simulator · Horror · First-Person

Outlast
Shared: First-Person · Horror · Psychological Horror

Fears to Fathom - Ironbark Lookout
Shared: Horror · Psychological Horror · First-Person

Dagon: by H. P. Lovecraft
Shared: Horror · First-Person · Story Rich

KARMA: The Dark World
Shared: Walking Simulator · Horror · First-Person

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

Summer of '58
Shared: Horror · Walking Simulator · Psychological Horror

Welcome to Kowloon
Shared: Horror · Walking Simulator · Psychological Horror

Demonologist
Shared: Horror · Psychological Horror · First-Person

Visage
Shared: Horror · Psychological Horror · First-Person

The Beast Inside
Shared: Horror · First-Person · Adventure