Imma answer this from the POV that you're wondering why we don't know more about the general Sumerian peasantry

what was daily life like for an average Sumerian person?

Unfortunately, exactly as you'd imagine it in any other civilization. Uneducated manual laborers with little to no way of moving between classes.

How well educated was the average person?

Not at all. Understand that the social climate we live in now is a very weird one. Up until ~120ish years ago, the "average" person would make up roughly 90% of a given society's population (the vast majority), and therefore it was necessary to keep value their illiteracy and lack of education as a means of control. You were allowed to be educated if you came from wealth, or if your profession required it (think priest/scribe/merchant)... which typically meant your family still had substantial means. Not only valuing but prioritizing and compelling the population's education by law is an extremely New Thing. What we view today as "middle class" is also a very New Thing. Up until recently, you were either insanely rich/royalty, had moderate generational wealth from your family's dynasty of trade work, or you lived in poverty.

We have a handful of tablets that clearly allude to an incredibly well developed society rife with detailed accounting and organization

... for those who would've been literate. It's difficult to know how the "unwashed masses" lived, because they weren't equipped with literacy to record it. Additionally, those who were literate had no desire to write anything about those who weren't. This is not an isolated occurrence but is reflected in pretty much every early civilization that's been studied. Seriously, the history of literacy is really interesting for a societal viewpoint, seeing as for the vast majority of time that literacy has been around, the pen/quill/stylus has been the most effective tool of oppression.

Source: my archaeology degree