A small set-top box (essentially a Steam Deck with the screen, controls and batteries removed, and with components that don’t have the space restrictions that come with a mobile device) would still be an interesting proposition. Particularly if they partnered with the main video streaming services to port their apps across, and implemented Chromecast/AirPlay support.

I can see a market for it, as a “Chromecast and Apple TV competitor that also plays all your games”.

Valve’s Proton is open source but is it also free to use and distribute in commercial software?

Yes.

Valve’s Proton code is licensed under the BSD licence, which is a “do anything you like with this code” licence.

Wine code is under the LGPL. You can ship this in commercial software as long as you “make the source code available” (which, assuming the distributor isn’t modifying the Wine code further, can be achieved by just linking people back to the main Wine project code repository).

DXVK is licensed under zlib, which is functionally the same as the BSD licence.

If you’re using Raspbian, any of the Debian family will suit you.

Ubuntu is still an excellent choice, despite the hipster hate. It comes in many flavours.

Vanilla Debian is absolutely fine for Steam-based gaming.

Pop!_OS, Mint & Zorin all have big followings. There’s also MX.

Take your pick, really.