Games like Sir Bucket
Games like Sir Bucket include The Henry Stickmin Collection, Road 96: Mile 0, Reventure, Undertale, and The Stanley Parable. We matched them by the tags players give Sir Bucket on Steam (Choose Your Own Adventure, Exploration, Interactive Fiction, Walking Simulator, and 2D): closest matches first, and among equally close ones the better-known games.

The Henry Stickmin Collection
Shared: Choose Your Own Adventure · Multiple Endings · Funny

Road 96: Mile 0
Shared: Choose Your Own Adventure · Exploration · Interactive Fiction

Reventure
Shared: 2D · Multiple Endings · Exploration

Undertale
Shared: Multiple Endings · Choices Matter · 2D

The Stanley Parable
Shared: Walking Simulator · Exploration · Multiple Endings

THE LONGING
Shared: Choose Your Own Adventure · Walking Simulator · 2D

Breakout 13
Shared: Choose Your Own Adventure · Interactive Fiction · Exploration

60 Seconds! Reatomized
Shared: Choose Your Own Adventure · 2D · Exploration

Late Shift
Shared: Choose Your Own Adventure · Interactive Fiction · Choices Matter

Road 96
Shared: Choose Your Own Adventure · Choices Matter · Multiple Endings

Until Dawn™
Shared: Choose Your Own Adventure · Interactive Fiction · Multiple Endings

Firewatch
Shared: Walking Simulator · Exploration · Story Rich

Suzerain
Shared: Choose Your Own Adventure · Interactive Fiction · Choices Matter

I Wani Hug that Gator!
Shared: Choose Your Own Adventure · Interactive Fiction · Choices Matter

60 Seconds!
Shared: Choose Your Own Adventure · Exploration · 2D

Endless Monday: Dreams and Deadlines
Shared: Choose Your Own Adventure · Interactive Fiction · 2D

Pentiment
Shared: Interactive Fiction · Exploration · Choose Your Own Adventure

While We Wait Here
Shared: Choose Your Own Adventure · Walking Simulator · Multiple Endings

CARIMARA: Beneath the forlorn limbs
Shared: Exploration · 3D · Walking Simulator

80 Days
Shared: Choose Your Own Adventure · Interactive Fiction · Choices Matter

The Wolf Among Us
Shared: Choose Your Own Adventure · Multiple Endings · Choices Matter

Far Away
Shared: Choose Your Own Adventure · Choices Matter · Interactive Fiction

Mirror 2: Project X
Shared: 3D · Interactive Fiction · Multiple Endings

Refind Self: The Personality Test Game
Shared: Interactive Fiction · Choose Your Own Adventure · 2D