How do drummers manage 4 different rhythms within their own one body?

Practice.
Pianists are the same.

Car drivers are the same too (basically (at least the stick shift drivers)).
Your right foot handles the accelerator, and the brake, your left the clutch.
Your hands control the steer, but also sometimes one hand changes radio stations, handles the indicator, fights a wasp, all the while keeping the other hand on the wheel.
This all in unison.
So, in a way you are already a starting drummer (if you drive cars).
Just add rhythm.

Good analogy. I used to drive a stick.

That’s what makes drummers so special. Not everybody can do it. It’s like being a really good bassist, too. (Not omitting the talent it takes to be a good guitarist, or any other really good musician.)

It does seem quite a bit more complicated than driving a stick.

I play stringed instruments, and my left hand and right hand are doing two different things. Often my leg is tapping along the rhythm. So that’s three limbs. It’s not too much of a stretch to do a 4th limb. The stick shift analogy is great.

My teacher uses the “tapping head and rubbing belly” example all the time when I’m struggling to learn something new.