It would make sense they seek to get as close as possible to that goal without actually engaging the caliphate, that makes sense.
Alternatively, they puppet the caliphate against Iran which would imply something more limited in terms of actual occupation but evidenced by freedom of action beyond their declared boundaries while supplying arms. A giveaway would be any kind of joint operation that limits Hezbollah.
There is a significant community of Korean ethnic origin in Russia as well.
If units of entirely Korean ethnicity were in Kursk we would have seen drone strike videos by now.