In what universe can a 100,000 man army launch attacks against your neighbor whilst operating out of your home country funded and manned by your nation and not be at war?
It would be like having the Texas national guard launching rockets into Mexico. The US and Mexico would be at war. Proxy war as a sub for actual war only works when you are strong enough your adversary is disinclined to respond to your provocation. Imagine hiring goons and visibly directing them to break your neighbors windows and thinking that you can stay out of the scuffle.
Critique Israel all you like and I do as well. I don’t feel like Lebanon has any right to complain that Israel is striking them. They should commit to stopping the attacks and they and Israel should make peace.
Yes any country that hosts a terrorist militia should both shut it down and make peace with its neighbors. Israel should offer peace in exchange for all hostages and a lawfully administered democratic Palestinian state protected by the UN but without arms for a period of time. Unlawful Israeli settlements should be ceded to this state.
All these things are worth doing and benefit everyone except hard liners on both side which have aspirations that range from unlawful to unrealistic.
Instead of achieving any extreme ends of either party the results of current strategy is likely to be a permanent state of suffering that will directly or indirectly harm millions. Their lifes and times are worth saving.