Games like DeskPet
Games like DeskPet include Stardew Valley, Potion Craft: Alchemist Simulator, Chinese Parents, Volcano Princess, and My Time at Portia. We matched them by the tags players give DeskPet on Steam (Casual, Simulation, RPG, God Game, and Dating Sim): closest matches first, and among equally close ones the better-known games.

Stardew Valley
Shared: RPG · Simulation · Life Sim

Potion Craft: Alchemist Simulator
Shared: Simulation · Crafting · Casual

Chinese Parents
Shared: Simulation · Casual · RPG

Volcano Princess
Shared: RPG · Simulation · Dating Sim

My Time at Portia
Shared: RPG · Simulation · Casual

Fields of Mistria
Shared: RPG · Dating Sim · Simulation

Coral Island
Shared: Simulation · Dating Sim · RPG

Touhou Mystia's Izakaya
Shared: Casual · Simulation · RPG

STORY OF SEASONS: Friends of Mineral Town
Shared: Simulation · Casual · RPG

The Sims™ 4
Shared: Simulation · Casual · Dating Sim

鬼谷八荒 Tale of Immortal
Shared: Simulation · RPG · Dating Sim

Sun Haven
Shared: RPG · Dating Sim · Simulation

Mountain
Shared: Simulation · Casual · God Game

The Sims™ 3
Shared: Simulation · Casual · RPG

Sword and Fairy Inn 2
Shared: Casual · Simulation · RPG

LoveChoice
Shared: Dating Sim · Simulation · Casual

Matchmaking Inc.
Shared: Casual · RPG · Dating Sim

Retirement Simulator
Shared: Simulation · RPG · Casual

My Time at Sandrock
Shared: Dating Sim · RPG · Crafting

Graveyard Keeper
Shared: RPG · Simulation · Crafting

Melvor Idle
Shared: Casual · RPG · 2D

SPORE™
Shared: God Game · Simulation · Casual

Potionomics
Shared: Simulation · Dating Sim · RPG

I Am Future: Cozy Apocalypse Survival
Shared: Casual · RPG · Simulation