I game on Linux. Can you play your entire Steam library on it? New. Is any game likely to work on Linux? Hell yes!
Some games have anti-cheat running in the kernel on Windows (on Linux it doesn’t run there, and you’d rather not). For that anti-cheat Linux support must be enabled by the developer. This can be done either by making a native Linux version of it, because we are Linux versions of these anti-cheats, or by turning on Proton support in the Windows version. Fortnite (well, no Steam) has BattlEye and EAC, and has deliberately disabled Linux support. Apex Legends has EAC with Linux support on. Arma 3 has BattlEye with Linux support on.
When a game doesn’t work, kernel-space anti-cheat is usually the reason. But otherwise you very rarely have a game where the issue lies elsewhere. In my experience there are very few, but every now and then you do have them. In practice, my games always work, provided there is no annoying anti-cheat in them. But your mileage may vary.
In terms of performance, it will sometimes change. Native is in principle the best, because WINE remains a translation layer that in principle adds an extra action. Nevertheless, there are games that run better in WINE than on Windows. I believe one of the Final Fantasy games implemented DirectX incorrectly making it run poorly on Windows, but WINE again had performance optimizations so it wasn’t an issue there. I should look it up, but I believe it had to do with multithreading being turned off. That is more the exception than the rule. Not every native port is created equal. The Witcher 2 had a really bad port when the Linux version was new, although I believe it was fixed years ago now. It is my expectation that if a Linux version and a Windows version of a game are both well made, the Linux version would be faster. Simply because Linux has less overhead. But there are quite a few other factors that play a stronger role, so that rarely turns out to be the case in practice.