Desktop mode on the Steam Deck is using KDE Plasma. You can use that on the vast majority of Linux distros.
Here is a few the spring to mind:
- Bazzite - A good place to start, their project goal is to basically be SteamOS like experience you can put on any machine.
- Fedora Workstation with KDE - Bazzite is based off of this project, it's a more general experiance, lots of people enjoy it.
- Kubuntu - Ubuntu is very popular distro, this is their KDE version.
- OpenSuse Tumbleweed - For folks who want the most up to date software possible.