Quick answer: Developer pepsipu's ns2jb runs native code on Switch 2 system software 23.0.1 through the Switch 1 version of SmileBASIC. It's tethered, needs a computer on the same network, is cleared by a reboot and isn't custom firmware.
The Switch 2 has its first software-only jailbreak, and it doesn't need a modchip. Developer Sammy Hajhamid, known as pepsipu, calls it ns2jb and describes it in a blog write-up as, to the developer's knowledge, the first exploit of its kind for the console. It works on system software 23.0.1, the current version.
The exploit starts in the Switch 1 version of SmileBASIC 4, a programming app, running through the Switch 2's backward compatibility. From there it chains bugs until it can run native code with the permissions of system modules, including the built-in filesystem module. pepsipu says that allows homebrew, reverse engineering and modding Switch 2 games, and backing up save files off the console. To show it off, pepsipu modded Mario Kart World with new racers like Cinnamoroll, the red Angry Bird, Peter Griffin and Steve from Minecraft. pepsipu credits OpenAI's Codex with helping, and that the jailbreak itself took about two weeks of work.
There are big limits. ns2jb is tethered, so it has to be run again from SmileBASIC every time the console starts, and a restart clears it. The developer's instructions say it needs a computer on the same network as the console. It doesn't install custom firmware or anything persistent, though pepsipu hopes it helps the homebrew scene work toward custom firmware.
Notebookcheck reports that developer Gezine, who recently revealed a separate Switch exploit, said he spoke with pepsipu and that the work "seems legit." The Verge notes the process still looks very complex for most people, and its full impact isn't clear yet.