Games like STAY
Games like STAY include Cyber Manhunt, Mandate Of Heaven, Stardew Valley, 鬼谷八荒 Tale of Immortal, and Little Witch in the Woods. We matched them by genre: closest matches first, and among equally close ones the better-known games.

Cyber Manhunt
Shared: Simulation · RPG · Puzzle

Mandate Of Heaven
Shared: RPG · Simulation · Puzzle

Stardew Valley
Shared: RPG · Simulation

鬼谷八荒 Tale of Immortal
Shared: Simulation · RPG

Little Witch in the Woods
Shared: Simulation · Puzzle · RPG

Crusader Kings III
Shared: Simulation · RPG

Total War: WARHAMMER
Shared: RPG · Simulation

Unheard - Voices of Crime
Shared: Puzzle · RPG · Simulation

Graveyard Keeper
Shared: RPG · Simulation

Amazing Cultivation Simulator
Shared: Simulation · RPG

Sanfu
Shared: RPG · Puzzle

Touhou Mystia's Izakaya
Shared: Simulation · RPG

Papers, Please
Shared: Simulation · Puzzle

CaseCracker
Shared: Puzzle · RPG · Simulation

My Time at Portia
Shared: RPG · Simulation

Pretty Neko
Shared: Simulation · RPG · Puzzle

Chinese Parents
Shared: Simulation · RPG · Puzzle

Crazy Machines 3
Shared: Simulation · Puzzle

龙胤立志传
Shared: RPG · Simulation

Niche - a genetics survival game
Shared: Puzzle · RPG · Simulation

Fate Seeker II
Shared: RPG · Puzzle

Kenshi
Shared: RPG · Simulation

Bridge Constructor Portal
Shared: Puzzle · Simulation

Mini Motorways
Shared: Simulation · Puzzle