With Linux gaming clearly showing it’s becoming more popular, and with GOG under new ownership, there’s hope yet that GOG will improve their Linux support.
GOG does currently support Linux — well, kind of. They publish Native Linux packages for various games, which depends on the developer (just like Steam does without Proton) but they have a very limited support of distributions, which can cause problems installing Linux games from GOG due to dependency mess. That, and GOG Galaxy does not support Linux.
There’s easier ways to install games from GOG on Linux / SteamOS though, which you can check out in our GamingOnLinux Guide. You can even do it directly in Steam if you want to.
They could, but Heroic already does pretty much everything an official client would do, I don’t think it makes sense to create a new client.
I don’t think it really makes sense to create Proton forks for specific games outside very specific cases (like hacky fixes that break other games). Might as well just upstream whatever changes you make.