If you're interested, here's a video of when a youtuber did it live on a 5900x about a year ago. They go into fine detail about the process.

https://www.youtube.com/watch?v=ISmyfzlf8SY

You use Vaseline, electrical tape and duct tape, paper towels, and good airflow for extreme overclocking. And there will be condensation, but a motherboard won’t last long anyways, burnt out vrms and fried cpus

You cover it with kneaded eraser or petroleum jelly or some other sealer, and cover that with lots of towels.

You could use one of those non-conductive liquids [1]. They have products with pour points going down below -100C. Depending on the interface between the liquid nitrogen and the coolant it might still flow well.

[1] https://www.3m.com/3M/en_US/data-center-us/applications/imme...

you prepare it using wax/conformal coating (+towels) - it's quite a standard procedure for sub-ambient cooling.

Insulation. Here you can see the motherboard getting prepared for LN2 overlock: https://www.tomshardware.com/reviews/overclocking-amd-ryzen-...

You can see on the pictures the MB is modded to avoid this.

The other answers all cover the prep, but the other key part here is you just don't run like this for very long. You run in like 1 hour bursts, and let everything dry out (and warm back up) between runs. So you're just not giving condensation enough time to build up enough to cause shorts in the areas that are not fully sealed off, or at least that's what you're banking on.

Can extremely dry air be used for it, or will it have some other side effects on Thermal conductivity?

Well, partially with good insulation, Vaseline or plastidip coating.

And partially, you just don't. It'll freeze over and since this is for competition and not daily use, that is okay. Usually nothing gets damaged, sometimes it does. Extreme OC is expensive.

You apply a conformal coating to the PCB.