Dogs will stare at you or something directly in front of them while they are pooping as a natural defense instinct.
The dog is not really embarrassed to be pooping in front of you and it's usually not the reason they are staring at you while pooping.
But instead the dog is staring at you to be sure that everything is okay around them while they poop and is just a natural instinct that the dogs are born with and have been that way since the dogs have lived out in the wild.
It can also mean that the dog is trusting you to protect them while pooping even though pooping in humans is embarrassing for some reason.
I cannot poop in a public toilet if someone else is in the restroom with me even though we all poop it has just always been embarrassing for some reason.
I have to wait until nobody else is in the bathroom with me to poop.