Games like Oblivion
Games like Oblivion include MiSide, Poppy Playtime, Ready or Not, Escape the Backrooms, and Resident Evil Requiem. We matched them by the tags players give Oblivion on Steam (Horror, Singleplayer, Psychological Horror, FPS, and 3D): closest matches first, and among equally close ones the better-known games.

MiSide
Shared: Psychological Horror · Horror · Singleplayer

Poppy Playtime
Shared: Horror · Singleplayer · Psychological Horror

Ready or Not
Shared: FPS · Singleplayer · Horror

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

Resident Evil Requiem
Shared: Horror · FPS · Singleplayer

Garten of Banban
Shared: Horror · Singleplayer · Psychological Horror

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

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

Outlast
Shared: Horror · Psychological Horror · Singleplayer

Choo-Choo Charles
Shared: Horror · Singleplayer · First-Person

Buckshot Roulette
Shared: Horror · Singleplayer · First-Person

Little Nightmares II
Shared: Horror · Singleplayer · Adventure

Firework
Shared: Horror · Psychological Horror · Singleplayer

Demonologist
Shared: Horror · Psychological Horror · First-Person

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

Subliminal
Shared: Singleplayer · Psychological Horror · Horror

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

Resident Evil 7 Biohazard
Shared: Horror · Singleplayer · First-Person

Resident Evil Village
Shared: Horror · Singleplayer · First-Person

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

Atomic Heart
Shared: FPS · Singleplayer · Adventure

ParanormalHK
Shared: Horror · Psychological Horror · Adventure

Outlast 2
Shared: Horror · Psychological Horror · Singleplayer

Garten of Banban 2
Shared: Horror · Singleplayer · Psychological Horror