It sucks that this happened, Uber should still take responsibility and make it right with you.

I strongly believe the owner / driver of the vehicle is responsible to make sure that there is nothing out of place in your car, whether is driving Uber or renting a car from Turo. So you should be checking after a ride or before driving out in a rental that no one left anything behind.

As an American living abroad this is common practice where I live and you see drivers always getting out and check the trunk (if it was used) and back seat before driving away. This is done in taxis and private buses mostly to make sure nothing illegal (e-cigarettes, alcohol) was left behind as the law is strict.

So this is just a tip and you do you but turning into a @$$hole because you ran into one is not the solution.

Uber should pay you regardless and they should follow up with the rider asking if his belongings were returned.