Games like Happy Pet
Games like Happy Pet include Stardew Valley, Screen Cat, Unpacking, Sticky Business, and Minami Lane. We matched them by the tags players give Happy Pet on Steam (Casual, Simulation, Cats, 2D, and Interactive Fiction): closest matches first, and among equally close ones the better-known games.

Stardew Valley
Shared: Simulation · Life Sim · Pixel Graphics

Screen Cat
Shared: Casual · Cats · Simulation

Unpacking
Shared: Casual · Simulation · Cute

Sticky Business
Shared: Casual · Simulation · Relaxing

Minami Lane
Shared: Casual · Simulation · Life Sim

Cat Goes Fishing
Shared: Cats · 2D · Casual

Coffee Talk Episode 2: Hibiscus & Butterfly
Shared: Dialogue Heavy · Simulation · Interactive Fiction

Maltese's Fluffy Onsen
Shared: Simulation · Casual · Pixel Graphics

Coffee Talk
Shared: Dialogue Heavy · Casual · Pixel Graphics

Organized Inside
Shared: Casual · Simulation · 2D

Potion Craft: Alchemist Simulator
Shared: Simulation · 2D · Casual

DAVE THE DIVER
Shared: Casual · Pixel Graphics · Simulation

Little Witch in the Woods
Shared: Casual · Simulation · Life Sim

Calico
Shared: Casual · Cats · Simulation

Slime Rancher 2
Shared: Simulation · Casual · Cute

Shelldiver
Shared: Casual · Simulation · 2D

Meowjiro
Shared: Casual · Cats · Simulation

Click the Button
Shared: Casual · Simulation · Pixel Graphics

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

Papers, Please
Shared: Simulation · Pixel Graphics · Indie

Thrifty Business
Shared: Casual · Simulation · Cute

Touhou Mystia's Izakaya
Shared: Casual · Simulation · Pixel Graphics

Placid Plastic Duck Simulator
Shared: Casual · Simulation · Cute

Digseum
Shared: Casual · Simulation · Pixel Graphics