The only one i used is CachyOS so its the best out of the three

My best experience with gaming on linux was on nobara(gnome)

Don't game much but I'll pitch in with a different suggestion: Debian minimal install or Arch, same as for every use case.

I prefer apt based distros so I always go Debian, but with flatpak it's basically irrelevant afaik.

I've had no trouble mimicking my deck's setup and game compatibility on basically any distro, use gamescope, proton etc.

Debian isn't bleeding edge but it also just werks and with flatpak I haven't encountered any issues getting new stuff essentially totally segregated from the main OS then nuking it if anything is borked without reinstalls or any downtime.

I'm quite new to linux gaming, and so far I've only used CachyOS and EndeavourOS.
I have a dedicated gaming computer with an AMD GPU, only one hard drive and no critical data. Both were easy to install but I just used the default options, didn't try to do anything complicated.
Performance-wise, I didn't see any difference (but I don't care enough to run benchmarks so maybe one gives me 3% more FPS than the other). I play in 1440p.
I've had a few mishaps on CachyOS regarding updates (2 years ago) so I tried EndeavourOS and it's all been smooth since then.

I guess the answer to your questions depends a lot on your gaming style and on what is important to you.
If you're like me, you just want it to work and you do nothing else than gaming, then all the distros mentioned in this thread are about as good.
If you want to squeeze that extra 2 FPS, or if you want to game on older hardware, or if you also use that computer as part of your homelab... then there are going to be differences.
You might want to consider giving us more information on your needs/projects so that we can adjust our answers.

Welcome to linux gaming :)

I’ve had good luck with Garuda after nearly two decades on Ubuntu and its derivatives.

So much so that I moved my work os to it, despite the gaming bent.

I've been pretty happy with Garuda Linux, Arch based. You'd be fine with near any of them though. Fedora base is amazing and stable and as well as the Arch based systems I use.

In the end it comes down to your hardware and what kind of gaming you want to do.
AMD gpus seem to work the best next with Intel GPUs. Nvidia can certainly work and be stable but has some drawbacks with Wayland from what I remember. (Maybe have been fixed?)

Anticheat is a crap shoot sometimes

I used EndeavourOS for about a year and a half with no issues at all. Currently testing Nobara as I wanted to try something different. Again, no issues at all.

There isn't "a best" exactly.

There are some things to consider though.

1. What hardware are you using?
2. Are the latest Video Drivers available for the distro you are considering?
3. How much configuration do you want to do?

Its a nuanced question. There isn't a 1 size fits all approach to this.

For me, going Arch was the move. It fit my usage habits.

I use Zorin OS, which is based on Ubuntu. Never had to set anything extra up, just installed Steam and everything worked.

Just my opinions as I am still a Linux noob (been using it on and off for the last 15 years, but only on old hardware, and I made A LOT of mistakes):

Handheld? --> Bazzite

Desktop? --> openSUSE Tumbleweed