There’s a field that was called Gu-edin in the mid third millennium BCE that was the subject of a border war that lasted a couple centuries, between the cities of Lagash and Umma (which is right where you said), because the founder of Lagash bought an unassuming piece of land from Umma and a bunch of surrounding terrains, and then did mad irrigation work and it became crazy fertile. According to Lagash’s records, Umma got mad that it was swindled out of such great land and kept attacking Lagash over it, and kept getting its ass kicked and its kings killed. People from Umma were “allowed” to till the field for Lagash for a time, but most of the grain would still go to Lagash, causing more revolts from Umma (and more punishment).

It’s fairly agreed that this place probably gave some degree of inspiration for “Eden”, along with some rare green gardens in the region created with irrigation work. The apple bit, the woman rib bit, and the knowledge bit came from other Sumerian myths.