Games like Haunted Mansion
Games like Haunted Mansion include Phasmophobia, Who's Lila?, Escape the Backrooms, MiSide, and Berry Bury Berry. We matched them by the tags players give Haunted Mansion on Steam (Horror, Psychological Horror, Surreal, Interactive Fiction, and Dynamic Narration): closest matches first, and among equally close ones the better-known games.

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

Who's Lila?
Shared: Horror · Psychological Horror · Choose Your Own Adventure

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

MiSide
Shared: Psychological Horror · Horror · First-Person

Berry Bury Berry
Shared: Psychological Horror · Surreal · First-Person

Demonologist
Shared: Horror · Psychological Horror · First-Person

Slay the Princess — The Pristine Cut
Shared: Psychological Horror · Horror · Choose Your Own Adventure

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

Gorilla Tag
Shared: Psychological Horror · Horror · First-Person

The Exit 8
Shared: Horror · Psychological Horror · Surreal

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

Mouthwashing
Shared: Horror · Psychological Horror · Surreal

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

Outlast
Shared: Horror · Psychological Horror · First-Person

Buckshot Roulette
Shared: Horror · First-Person · Psychological Horror

Amanda the Adventurer
Shared: Horror · First-Person · Interactive Fiction

Iron Lung
Shared: Horror · Psychological Horror · First-Person

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

CloverPit
Shared: Psychological Horror · Horror · First-Person

Pacify
Shared: Horror · Psychological Horror · First-Person

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

The Outlast Trials
Shared: Horror · Psychological Horror · First-Person

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

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