Games like Inner Ashes
Games like Inner Ashes include What Remains of Edith Finch, Firewatch, The Beginner's Guide, Outer Wilds, and Layers of Fear (2016). We matched them by the tags players give Inner Ashes on Steam (Adventure, Atmospheric, Story Rich, Walking Simulator, and First-Person): closest matches first, and among equally close ones the better-known games.

What Remains of Edith Finch
Shared: Atmospheric · Story Rich · Walking Simulator

Firewatch
Shared: Adventure · Atmospheric · Story Rich

The Beginner's Guide
Shared: Story Rich · Atmospheric · Walking Simulator

Outer Wilds
Shared: Adventure · Story Rich · Atmospheric

Layers of Fear (2016)
Shared: Atmospheric · Walking Simulator · First-Person

Call of the Sea
Shared: Adventure · Story Rich · Puzzle

Brothers - A Tale of Two Sons
Shared: Adventure · Atmospheric · Story Rich

Riven
Shared: Adventure · Puzzle · First-Person

The Witness
Shared: Puzzle · First-Person · Atmospheric

The Room
Shared: Atmospheric · Adventure · Puzzle

INFRA
Shared: Atmospheric · Adventure · Puzzle

Return of the Obra Dinn
Shared: Story Rich · Atmospheric · Puzzle

Gone Home
Shared: Walking Simulator · Atmospheric · Story Rich

Little Nightmares
Shared: Atmospheric · Adventure · Singleplayer

Quern - Undying Thoughts
Shared: Adventure · Atmospheric · Puzzle

Amnesia: A Machine For Pigs
Shared: Story Rich · Atmospheric · Walking Simulator

Obduction
Shared: Adventure · Puzzle · First-Person

The Talos Principle
Shared: Puzzle · Story Rich · First-Person

Hellblade: Senua's Sacrifice
Shared: Atmospheric · Story Rich · Adventure

SOMA
Shared: Atmospheric · Story Rich · First-Person

Before Your Eyes
Shared: Story Rich · Emotional · First-Person

Little Nightmares II
Shared: Adventure · Atmospheric · Puzzle

OneShot
Shared: Story Rich · Atmospheric · Adventure

Sally Face - Episode One
Shared: Story Rich · Adventure · Atmospheric