Linux Gaming

From your list I ran the following:

• Bazzite: worked AMAZINGLY (to the point of me double-checking whether I'm getting any updates 😆) until some image screwed up the boot process (some versions I could boot into, some were crapping out right after GRUB). Can recommend if you have a relatively normal hardware configuration (so, as long as your machine is not a Clevo-reseller laptop with NVIDIA GPU and Intel CPU, you should be fine).
  • Addendum: some binaries might not be available for you OOTB due to Bazzite's root filesystem being immutable. Read their docs on how to run packages / binaries that do require root access (or learn basics of self-hosting, I guess..?).
• Nobara: FUBAR'd it myself through... Well, being an idiot (had SOME regrets about that 😅); ran into some small issues with GPG keys, but otherwise used it w/o any major problems (see above) for... I think a year with some change? Can wholeheartedly recommend it, as long as you're somewhat familiar with what RPM packages are and how to work around issues with their signatures (usually - a trivial matter); updates are not as smooth as on Bazzite.
• CachyOS: my current daily driver. Barring some extremely minor issues in some games (usually solvable through Proton options- and versions fiddling), as was the case with Nobara - can wholeheartedly recommend it (this time, without caveats; despite the memery around Arch, it feels stable; the updates by default are a bit more annoying than on Bazzite though, similar in nature to Nobara: you get a notification "X packages have updates").