Games like Switchboard
Games like Switchboard include Death and Taxes, Papers, Please, Detroit: Become Human, Portal 2, and The Wolf Among Us. We matched them by the tags players give Switchboard on Steam (Story Rich, Puzzle, Adventure, Simulation, and Choices Matter): closest matches first, and among equally close ones the better-known games.

Death and Taxes
Shared: Story Rich · Choices Matter · Simulation

Papers, Please
Shared: Simulation · Point & Click · Puzzle

Detroit: Become Human
Shared: Story Rich · Choices Matter · Multiple Endings

Portal 2
Shared: Puzzle · Story Rich · Female Protagonist

The Wolf Among Us
Shared: Story Rich · Adventure · Choices Matter

OneShot
Shared: Story Rich · Puzzle · Adventure

Fran Bow
Shared: Story Rich · Puzzle · Point & Click

Road 96
Shared: Story Rich · Adventure · Choices Matter

Chants of Sennaar
Shared: Puzzle · Adventure · Point & Click

There Is No Game: Wrong Dimension
Shared: Puzzle · Adventure · Point & Click

The Room 4: Old Sins
Shared: Puzzle · Adventure · Point & Click

The Walking Dead: Season Two
Shared: Story Rich · Adventure · Point & Click

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

Little Misfortune
Shared: Story Rich · Adventure · Point & Click

Life is Strange: Before the Storm
Shared: Story Rich · Choices Matter · Female Protagonist

The Silent Age
Shared: Adventure · Story Rich · Point & Click

Not For Broadcast
Shared: Adventure · Choices Matter · Simulation

Myst
Shared: Puzzle · Adventure · Story Rich

The Room Three
Shared: Puzzle · Adventure · Point & Click

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

Road to Empress I
Shared: Story Rich · Choices Matter · Female Protagonist

The Walking Dead
Shared: Story Rich · Adventure · Point & Click

The Test
Shared: Story Rich · Simulation · Multiple Endings

Syberia: The World Before
Shared: Story Rich · Adventure · Puzzle