There isn't much they can do to foster native Linux support beyond trying to increase the number of people gaming on Linux. It's a chicken-and-egg problem, and you need to make the platform desirable to developers before they will start developing for it.
This is the chicken-and-egg problem though. If you don't get the Linux/Steam Deck audience large enough first, then that tradeoff won't be worth it to developers.
Valve have the money to pay developers to make a Linux port or ensure it works with Proton (maybe they already do in some cases?), if they really wanted to put the heat on Microsoft. Well, any not owned or being published by Microsoft i suppose.
Valve seem happy to let things happen more organically however.
