[wickerman]

Not sure about mesopotamia but there's evidence of indoor plumbing for sewage distribution in Knossos (Minoan civilisation - 3000 BC to 1100 BC).

https://en.wikipedia.org/wiki/Minoan_civilization#Plumbing

There's also plenty of examples of different kind of early toilets/sewage systems from 3000 BC in different cultures: https://en.wikipedia.org/wiki/History_of_water_supply_and_sa...

I think you're conflating an image of victorian england with a world that existed 4000 years before.

Edit: as says the wikipedia article:

The Mesopotamians introduced the world to clay sewer pipes around 4000 BCE, with the earliest examples found in the Temple of Bel at Nippur and at Eshnunna,[13] utilised to remove wastewater from sites, and capture rainwater, in wells. The city or Uruk also demonstrate the first examples of brick constructed Latrines, from 3200 BCE.[14][15] Clay pipes were later used in the Hittite city of Hattusa.[16] They had easily detachable and replaceable segments, and allowed for cleaning.