Is it fair to say that any game that runs on the Steam runs on Steam Linux?
No, it’s not that far along. A lot works, but if there’s invasive DRM or anticheat then it probably won’t. If you have specific games you want to play in mind check out https://www.protondb.com/
I know the variations have gotten better over the years but haven’t done too much research into it.
If you’re curious you can just create a live USB stick to test drive it. Won’t work well for gaming though.
The penguin must scream!