Surely all glue is edible, you just have to commit a bit more to some glues than others.
It's like that saying about mushrooms: "All mushrooms are edible. It's just that some mushrooms you only get to eat once."
I was taught “Edible (fit to be eaten as food) vs Eatable (capable of being chewed up and swallowed)” but modern usage seems to treat them as synonyms (the former just being more pleasant to eat than the latter).
I recently watched a video about death cap mushrooms (the deadliest, supposedly), and apparently about 80% of people still survive (requires prompt medical treatment), not that they would want to repeat the experiment. Apparently, the mushrooms even taste good.
Anyway, edible normally means "safe to eat," not just "possible to eat." (As you are no doubt aware). IIRC, Elmer's glue is considered safe to eat though not necessarily appetising.