not exactly action-packed or like Pinocchio but here are some recs
School 2013 - it explores violence, bullying, and male friendships
Shut Up: Flower Boy Band - Friendship, Loss of a friend and grieving; and bullying
Others:
Reply 1988 - ML has a brother with a health condition; it also explores friendships and when friends end up liking the same girl
Hwarang (a historical) - Friendship, rivalry, and teamwork. It also includes a side cast of 2 brothers who have different hierarchy within the family, thus one gets treated better & they don't get along as a result