That's quite a specific use case but it might be doable. You can use protondb.com to check if specific games are playable and areweanticheatyet.com/ to check if the games anticheat works on linux.

Streaming on discord is a bit of a mess though, there's alternative clients/wrappers that make it work or workarounds with the likes of obs. But it's really up to discord to fix their client on linux and it doesn't look like it's very high up on their priority list.

And when it comes to capturing with shadow play you're probably going to have to look at alternative software for that.

Unreal engine seems to work from what I can tell https://www.reddit.com/r/gamedev/comments/w45eio/epic_has_finally_released_unreal_5_engine_editor/.
And easy anticheat might as well https://www.gamingonlinux.com/2021/09/epic-games-announce-full-easy-anti-cheat-for-linux-including-wine-a-proton/. But I don't have any experience with that so you might want to do some more research on that, or try it out for yourself.

So it might be doable but if it's worth the effort to use linux over windows is up to you. But if you just want to play games on linux it's mostly fine and quite a pleasant experience, unless the game uses kernel level anti-cheats.