While I presume they don't provide a native Linux build, it is listed as Playable on Steam Deck.
> Valve's testing indicates that Blue Prince is Playable on Steam Deck. This game is functional on Steam Deck, but might require extra effort to interact with or configure.
> • Some in-game text is small and may be difficult to read
> • All functionality is accessible when using the default controller configuration
> • This game shows Steam Deck controller icons
> • This game's default graphics configuration performs well on Steam Deck
> Valve's testing indicates that Blue Prince is Playable on Steam Deck. This game is functional on Steam Deck, but might require extra effort to interact with or configure.
> • Some in-game text is small and may be difficult to read
> • All functionality is accessible when using the default controller configuration
> • This game shows Steam Deck controller icons
> • This game's default graphics configuration performs well on Steam Deck