You might ask why Iran would do this. As it turns out, sponsoring terror is an extremely cost effective form of international diplomacy. Instead of spending billions on defense to attack and intimidate regional rivals, the government of Iran can spend several orders of magnitude less, say a few hundred million in guns and cash for extremist groups.
Iran doesn’t have to recruit or pay the soldiers, because someone else will do it for them; doesn’t have to finance or strategize an invasion, because the militants are already in the enemy’s territory; doesn’t have to face moral culpability on the world stage, because they can claim clean hands.
This is not just ideological for Iran. It is simple dollars and cents (or rials). Persia is a 5000 year old civilization, and they are happy to gradually carve away at their enemies until there’s nothing left.