Sorry if this is getting into TMI territory but how does the bidet avoid dissolving the unwanted material and spraying it all over everywhere? And how does one dry this without toilet paper?

It works under the same principle as pressure washing, as long as the water pressure is high enough the final result is completely clean. Too high pressure can lead to material flying around everywhere but there's a very large range where the pressure is high enough to clean you but not enough to spray things around.

Drying is a personal preference and isn't as important anymore as you're clean down there now. Toilet paper is one option but you don't have to do it (I don't dry for reference) as it'll dry out by itself in a few minutes once you put your underwear on to absorb the water (which is fine because you're completely clean down there so it really is just clean water left).

By controlling the water pressure.

> And how does one dry this without toilet paper?

Normally you still use some small amount of toilet paper to dry away most of the water.