Games like Phantom Project
Games like Phantom Project include Poppy Playtime, DreadOut, Hellblade: Senua's Sacrifice, The Medium, and Little Nightmares. We matched them by the tags players give Phantom Project on Steam (Third Person, Supernatural, Singleplayer, Female Protagonist, and Horror): closest matches first, and among equally close ones the better-known games.

Poppy Playtime
Shared: Singleplayer · Horror · Free to Play

DreadOut
Shared: Third Person · Horror · Female Protagonist

Hellblade: Senua's Sacrifice
Shared: Female Protagonist · Singleplayer · Third Person

The Medium
Shared: Female Protagonist · Horror · Adventure

Little Nightmares
Shared: Horror · Singleplayer · Adventure

FATAL FRAME / PROJECT ZERO: Maiden of Black Water
Shared: Female Protagonist · Horror · Singleplayer

Tomb Raider Game of the Year
Shared: Third Person · Female Protagonist · Adventure

Sally Face - Episode One
Shared: Horror · Indie · Adventure

Alan Wake
Shared: Third Person · Horror · Adventure

Phasmophobia
Shared: Horror · Supernatural · Psychological Horror

Rise of the Tomb Raider™
Shared: Third Person · Singleplayer · Female Protagonist

Murdered: Soul Suspect
Shared: Supernatural · Adventure · Horror

Oxenfree
Shared: Supernatural · Female Protagonist · Indie

A Plague Tale: Innocence
Shared: Adventure · Female Protagonist · Third Person

The Mortuary Assistant
Shared: Supernatural · Horror · Singleplayer

Five Nights at Freddy's
Shared: Singleplayer · Horror · Indie

Dark Deception
Shared: Horror · Singleplayer · Free to Play

Resident Evil 3
Shared: Female Protagonist · Horror · Singleplayer

Little Nightmares II
Shared: Singleplayer · Horror · Adventure

Resident Evil 2
Shared: Singleplayer · Third Person · Horror

Outlast
Shared: Horror · Singleplayer · Adventure

Ultimate Custom Night
Shared: Singleplayer · Horror · Free to Play

Firework
Shared: Horror · Indie · Singleplayer

Fran Bow
Shared: Horror · Adventure · Singleplayer