I see no reason not to apply such adjectives to people who use weapons with such properties.

There are norms of the language, and I think that says it all. You can't say that a deep lake is shallow, or that a fat cat is wide, but that's exactly what your names are. And why can't elite archers be among humans? Are there only commoners there? And are elves some kind of aristocracy? )

I moved away from the word "heavy" precisely to get rid of the nonsense - because there are no "light" legionaries.

Of course, and you did the right thing. But legionaries, judging by your name, can be both armored and unarmored. If this is the case (which I doubt), then it would be more euphonious to call them heavy legionaries (because heavy legionaries are armored in this case, and light ones are not). If all legionaries wear armor, then there is no need to add anything else to them; the word "legionaries" already makes everything as clear as possible.

I couldn't find a better name for them. In the English version, it's Tornado Griffins, but you can't translate it like that into Russian.

It's simple: storm griffins, that's all.

Monastery governors.

Okay, but it's not obvious from the name. Not obvious at all. Maybe "guardian angels"?

An assassin is a professional killer, which a simple poisoner is not necessarily. But "poisoner" includes his specialization.

That's exactly what I said.

"Dungeons" do not convey the essence of the unit, but interceptors do. This unit is valuable primarily as an interceptor of enemy attacks. In battle, it has the "taunt" ability.

Okay. But again, it's not clear from the name.

Impulsive is very fitting for the "taste of blood" ability (+8 to attack and +2 to initiative for 1 round when taking damage).

It doesn't fit at all, it's not associated with it, it definitely needs to be replaced. If you don't like "furious," okay, but "impulsive" is a description of character, not combat abilities.