Right-wing religious fundamentalists like the current Netanyahu lead government in Israel thrive by creating hatred and dehumanising their perceived "enemies" to create an us vs them narrative to stay in political power. The terrorist strike and massacre in Israel was a blessing to the unpopular Netanyahu and his ilk, who were actually about to lose power in Israel. The war in gaza, and now the subsequent plan to enlarge the conflict to involve the other "enemies" of Israel is just a blatant power grab by the right-wing religious fundamentalists in Israel, and an attempt to fulfil their goals of creating a "Greater Israel".
Netanyahu's "grand plans" are however myopic and only guarantees misery in the region. While the US may support Israel to not lose such a war, there is no guarantee that Israel will win or come out better without a very high price- Russia has already started reinforcing Iraninan military with weapons as the sudden increase in Russian cargo flights to Iran suggests (and Russian media has reported). Turkey has publicly announced that if Israel widens the conflict, it will militarily commit itself to the Palestinian cause (one wonders how NATO will react to another NATO member fighting an American ally, and possibly even the Americans!). Despite the Hezbollahs being labelled as terrorists, they are a well organised military force armed with enough decent weapons to offer not only real resistance but also have offensive capabilities.
The best thing Israel can do is to pause the war, hold elections, and get rid of Netanyahu and the religious fundamentalists. Only the saner minds in Israel can prevent the region from getting ensnared into a vicious cycle of hate and misery for the next decade or two.