If you let one person get away that means others will also think they can get away with stealing. I know this is a story but theres an apocalypse going on, everything is scarce, you need control. Maybe what they should have done is exiled the guy let the zombies get him.
They said in the previous chapters that zombies don’t kill/eat people
This is true, it seems that they just can't die, but they also seem to be harbingers of disasters. You won't survive in a place WITH them, hence why they are secluded in the town, so going outside is pretty much a sentence to a slow and painful death filled with constant anxiety as to when the your luck will finally run out, then you'd most probably turn into a zombie too, coz no one ain't going anywhere in that limbo.
i know and i understand that, what I'm saying is killing isn’t the justified punishment
"Everyone agreed" ho that doesn't justify anything. I know that there is an apocalypse going on, but killing a person is not the first-line punishment for stealing. I guess being killed by a zombie is okay than being in the hands of a human that has no remorse geez