I do not read Musnad, let alone call myself an expert (A privilege only a few true erudite persons can call themselves, such as Dr. Juris Zarins; He cracked a hole in the myth of the "lost city of Ubar", by not only locating the site but also explaining the fragility of the myth), but I do imagine that most of it would be in the category that you have mentioned; Either homage or described religious ritual, inscribed into a larger, more publically available surface or media, or something less such as administrative documents, inventories and census (You know, for wages or assignments... An ideal example would be the Persepolis fortification or Elamite tablets, where we get a lot of formalities, basic arithmetics and so forth).

I would estimate that it is mostly administrative stuff (As they tend to be more abundant amongst civilizations that have depended mostly on archaeology rather than the classics as a main corpus of information), but then again, we must not understimate administrative literati, because they are the key in attesting the position of a scribe, but also attesting a viable format as well as basic math in the same context. It is in this boring, mundane stuff we get to appreciate the complexity of a society which puts enough weight and priority of importance to make such records.

As for literacy rates... I have this rather... I should say unorthodox perception (It is), but I believe that civilizations that prioritize commerce, and live at the cross-roads of several lingua franca, do by ethos have a higher literacy rate; Not because of the prevalence of education, but rather because of a contemporary form of social darwinism, compelling merchants to improve themselves by actively pursuing knowledge. Let us take the Parthians as an example; They knew how to handle the Chinese, and their mastery in keeping their lucrative trading contracts, by actually cheating them on correct information (Exaggeration of distances between the Han and the Romans, hazards of nomads, et al.). The Nabataeans and Sabaeans engaged in a similar contest when it came to dominance in the Red Sea, the Incense Route, the later Maritime Incense Route, and ultimately the shares in India.