Is 茂る a stative verb?

Question

Why don't dictionaries include this kind of things? Do Japanese ones do?

Answer 1

茂る is a punctual (instant state-change) verb (aka 瞬間動詞). That is, この森には様々な木が茂っている almost certainly means that the forest is full of (already-grown) various trees, not that various trees are in the process of growing now.

Why don't dictionaries include this kind of things?

Unlike the verb conjugation patterns (godan, ichidan, etc.), the differences between action/stative/punctual are often blurry, and it's almost impossible to perfectly categorize them. See discussions about 溶けている and 寝ている.

Do Japanese ones do?

Unfortunately, no.