We could go for ever if we want to trade 'who started it' stories, but Israel hitting an embassy was grounds for war from Iran. Israel crossed a line. Iran, as stated, would prefer to let their proxies do the dirty work, but by launching everything at the same time, giving Israel and it's partners time to address each wave separately, that indicates to me Iran didn't want to create great damage. Would they have preferred a few get through? Probably, but I think they expected most to get knocked down. On paper, they can still tout they fired so many to make it look impressive, but they wanted to no part in this, but felt they had to respond to a unprecedented attack on their embassy.
I agree with Biden's response to Israel, with multiple Muslim countries stepping up to defend Israel, Israel needs to accept it as a great win and see if it can't build from it with it's local partners.