As noted in a sibling comment, Valve has released an open-source compositor (`gamescope`), which is what presents Steam as a console-esque UI on the Steam Deck. Using gamescope to present Steam, you can make an arbitrary Linux feel indistinguishable from a Deck.
There are many gaming distributions (e.g. Bazzite, Jovian/NixOS, Nobara, Chimera…) that take this approach.
They're usually just standard desktop distributions (Fedora or NixOS) with gaming packages configured. There is a Russian teenager who's trying to cobble together a SteamOS clone using as many Valve packages as possible. His project is called HoloISO.
No, he's talking about the compositor which has several gaming related features which then runs the Big Picture version of Steam for UI to select and manage games.
They're right that the compositor is gamescope, it's made by Valve and it has game-related features, but the person 3 comment-levels above me did seem to be conflating gamescope with the Big Picture UI. You can absolutely use gamescope and not use Big Picture mode at all, lots of people using Wayland do so by wrapping their games in a call to gamescope.
There are many gaming distributions (e.g. Bazzite, Jovian/NixOS, Nobara, Chimera…) that take this approach.
They're usually just standard desktop distributions (Fedora or NixOS) with gaming packages configured. There is a Russian teenager who's trying to cobble together a SteamOS clone using as many Valve packages as possible. His project is called HoloISO.