We know it's not the entire extent because we also have a bunch of their literature and history in cuneiform. We even have some jokes! Although none of the ones I have read really survive the translation and time gap... at all. However, stuff like agricultural records are the bulk of it by the numbers simply because that was the stuff that was useful to ordinary people day to day
Oh, interesting! I suppose that makes sense, given that humans have been drinking beer for millennia longer than we've been writing. The first society to start writing probably would talk about beer a fair bit. I've seen prayers about and recipes for beer before (sometimes the same text), but not the one you described
Semi-related: when I went to have a look for texts about drunkenness, I learned about the Dialogue of Two Scribes. It's amazing. It's literally just 130+ lines of back-and-forth insults
Fun fact, mesopotamian beer was drank through a straw because they did not filter it. They'd simply let the solids fall to the bottom and sip off the liquid