On the other hand, Linux still lacks a gamepad-focused UX out of the box, which is the real selling proposition of this device. These handheld PC's are not inherently "gaming" machines, they could have all sorts of interesting enterprise-focused uses out in the field if we managed to find a nice way of centering the whole UX interaction on those weird chorded buttons and analog controls.
This is not true of SteamOS and Bazzite. The entire OS is controller supported. I have my desktop running Bazzite plugged in to the TV with no kb/m. Can do everything from updating the system, changing the screen resolution, formatting sd cards, etc with just a controller.
As for the enterprise part of OP's comment, Bazzite is a community-contributed OCI container (similar to a Docker container) running on top of a Fedora bootc spin with GNOME or KDE. It is trivial for a company to add their own RUN instructions to the OCI Containerfile.
Here's a working one that I prepared earlier that installs 1Password on Bazzite GNOME and Bluefin:
Bazzite does include the Steam frontend but that's a proprietary system, it's not something that the Linux/FLOSS community came up with. The KDE folks are starting to look into remote-control focused "10-foot" media center interfaces (see the Plasma Bigscreen project) that are also somewhat applicable to gamepad control (though these handheld devices generally come with touchscreens too, and this creates additional affordances) but that's a bit of a too little and too late situation. We need far more than that to make this novel class of devices usable for genuine production uses.
Heroic Launcher requires dropping down to desktop mode once to install the app. Once installed properly it appears as an app inside Steam, which you can launch and then install and play your GOG and Epic games.
I hardly ever do that, but the one time I did (for Minecraft) I did just drop down to desktop mode and used the trackpad and touch screen. This wasn’t really to do with Linux though. Minecraft does not provide any way to install and log in with controller support.
After I installed it one time, I added it to Steam and could launch and update it with a controller. In theory GOG could integrate with Bazzite to offer a controller friendly store and UI. But considering they haven’t even bothered with a desktop Linux client, I’m not holding my breath.
A Windows 11 gaming PC hooked up to a tv 100% needs a Mouse and Keyboard right now. You can't even sign in otherwise. This might change with their gamemode they are offering on these portables though.