i do like this idea
similar to how it shows ?i think? when youre playing a non-steam game added to library
or i think it used to. im not actually online anymore for it to show up
Now that Steam deck it's a thing, I think this resource it's even more useful, since people who are not familiar with Proton / Wine may try to contact the game developers directly about problems with it
And the official documentation stating this, means that developers doesn't necessary have responsibility on it

So it would be better if they know that their games are running though a compatibility tool in order to minimize this misunderstanding
Nothing extracted yet.
I want to suggest (if possible) the inclusion of some kind of information when someone is playing a game through a compatibility tool like proton, so other people know we're using it.
The reason is not many people outside the Linux bubble knows what Proton is, and this could drag some positive attention to this steam feature.
I suggest something like "Proton: nameofthegame" or the usage of a different shade of green / another color