Games like Possession
Games like Possession include Firewatch, What Remains of Edith Finch, Amnesia: A Machine For Pigs, SOMA, and Outer Wilds. We matched them by the tags players give Possession on Steam (Adventure, Walking Simulator, Exploration, First-Person, and 3D): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Adventure · Walking Simulator · First-Person

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

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

SOMA
Shared: Horror · Exploration · Atmospheric

Outer Wilds
Shared: Exploration · Adventure · Mystery

Outlast
Shared: First-Person · Horror · Atmospheric

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

Lethal Company
Shared: First-Person · Horror · Exploration

Five Nights at Freddy's: Security Breach
Shared: Horror · First-Person · Exploration

Escape the Backrooms
Shared: Horror · First-Person · Adventure

Scanner Sombre
Shared: Walking Simulator · Exploration · Adventure

Inside the Backrooms
Shared: Horror · Adventure · Exploration

The Forest
Shared: Adventure · Horror · First-Person

INFRA
Shared: Exploration · Walking Simulator · Adventure

CARIMARA: Beneath the forlorn limbs
Shared: Adventure · Exploration · Mystery

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

Still Wakes the Deep
Shared: Walking Simulator · Horror · First-Person

PEAK
Shared: Adventure · Exploration · First-Person

Psalm 5:9-13
Shared: Exploration · Walking Simulator · Horror

Gone Home
Shared: Walking Simulator · Exploration · First-Person

The Vanishing of Ethan Carter
Shared: Walking Simulator · Exploration · Adventure

Poppy Playtime
Shared: Horror · First-Person · Adventure

The Exit 8
Shared: Exploration · Walking Simulator · Horror

Five Nights at Freddy's: Secret of the Mimic
Shared: Adventure · First-Person · Horror