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.

This really depends on your definition of "stability".

The technical definition is "software packages don't change very often". This is what makes Debian a "stable" distro, and Arch an "unstable" one.

The more colloquial definition of "stability" is "doesn't break very often", which is what people usually mean when they ask for "stable" distributions. The main problem with recommending a distro like this, is that it's going to depend on you as a user, and also on your hardware.

I, personally, have used Arch for about 5 years now, and it's only ever broken because I've done something stupid. I stopped doing stupid things, and Arch hasn't broken since. However, I've also spoken to a few people who have had Arch break on them, but 9 times out of 10, they point to the Nvidia driver as the culprit, so it seems you'll have a better time if you have an AMD GPU, for example.

Debian testing (more up to date than ubuntu, rolling release, much more stable than the name suggests, truly free as in freedom)

What is your definition of stability? I have used Arch for about ten years without any major breakage, but sometimes you do have to do some manual tinkering if a package stops working. So it's stable enough for me, but maybe not for others. Since it is a rolling release, packages are generally being updated quite rapidly.

I think that any modern rolling release distro would fit the bill though.

The holy grail, stable and up-to-date, it exists, it's called Debian with Flatpaks.

Install Debian. Avoid doing any changes to your package selection, try to get things from flatpaks.

Devuan testing branch.

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.