I would recommend Bazzite. It’s based off of Fedora Silverblue and it’s what I currently use. Very stable compared to the others that I’ve tried. Choose “Bazzite Deck” when you install if you want it to boot directly into Steam game mode.
chimera is is a near drop in replacement for steam os built for being a gaming first distro. it isn't great if you want to do many other things with your desktop but works really well if you only want to game.
If you're just wanting the functionality of a Steamdeck on some other device, there are a variety of ways to accomplish that. If the other device is an Android, you can just install the Steam Link app and you're off to the races. If it's something else, depending on the device you can probably get Moonlight running on it, which will accomplish the same thing but will actually have more versatility than you'd get with a Steamdeck anyway.
You know that a steamdeck is actually running the game locally and not streaming it over a network, right? It can do that, but it has more versatility that you'd get from just Steam Link/Moonlight.
Yes, I'm just offering an option to replicate that streaming functionality here. As to versatility, that depends entirely on what you're doing. There are situations in which the Steamdeck would actually be the far more limited platform compared to what I described.