Linux

Could always install endeavouros and or arch if you prefer more work with btrfs and snapshots. Arch is mostly stable despite the laughter erupting from this post. Even if it does fall down you have the snapshots to fallback to in order to bail you out. Arch is like riding and steering a rocket but having btrfs is like having extra lives so crashing doesn't really kill you forever. Depends on what you want.

The good news is if you try arch long enough and spend hours tinkering with cutting edge software you too can come to the point where you are exhausted and just want a machine that does what the hell you want without screwing around with it. Or you can change your avatar to some sort of anime character and bask in the superiority of not only using arch but enjoying it like some sort of digital masochist.

By definition that's impossible, stable means packages don't get updated, so their version is stable. If you meant stability outside of the Linux world, as in "doesn't break" then most rolling release would fit, personally I use Manjaro, and have used Arch and Gentoo in the past, Tumbleweed is also a good option that others have recommended.

For what purpose though? All my servers and containers run debian. Everthing I care about publishes fresh packages for it, but on their own repos. My desktop and laptop run pop_os with a few additional repos.

Everything that needs to be bleeding edge can come from snap or flatpak these days anyway.

If you like Plasma or one of the other supported desktops, I suggest trying Siduction for this.

I'm also generally impressed by the packages available for Alpine Edge, if you're not bothered by a non systemd and non glibc distro.

Kubuntu (Ubuntu but KDE), both great KDE UI and stable kernel. I use Kubuntu LTS.

Slackware is as stable as it gets.

VanillaOS is pretty much what you're asking for. The only real downside right now is that Orchid probably won't have KDE support out of the gate

Gentoo, obviously.

I use it since it works. But it also has up to date packages. Number of times I tried moving away from it and it is just not possible.

I use Mint on side-desktop (one with graphic card I use for gaming and deep learning) and while it is easy to use it also has old software, python is stuck on 3.7 or 3.8 so it is becoming unusable even.

Will gentoo give you some problems? Probably, but those are always solvable and you will spend less time on other stuff.

Guix is a source based (rolling release) distro. Any package operation you do like like installing, updating, or removing, can be rolled back. So if an update ever breaks anything you can just roll-back and wait for the fix. You can even pin that specific package and continue to upgrade the rest of your system. And every state is saved in a generation, so you can go to any state your system has ever been in package/configuration wise.

Nix has all of these advantages as well.

Funtoo is a bit of both. It's not as current as Gentoo but the tradeoff is not having to rebuild the toolchain every few weeks.

Devuan testing branch.

I recommend using Manjaro KDE.