Fighting Hezballah in an attempt to destroy them or deal significant damage is practically mutually assurred destruction. There’s no real way they could wage the same type of warfare in Lebanon without incurring crippling damage to their infrastructure and a very high civilian death toll on both sides due to Hezb’s vast missile stockpiles and resources.
That attack is not justification for reckless escalation against the world’s most powerful non-state militia. There’s not much the Lebanese government can do to influence what would unfold and Hezb’s overall message since the start has been that hostilities in north are tied to hostilities in Gaza and will end once those end.
To me it does not seem like Hezb’s MO unless it was accidental and even then they’ve claimed responsibility for accidents in the past and there are miscellaneous militant groups that have launched missiles at Israel from Lebanon. Regardless of what you think of them, they generally act rationally from a military perspective. Either way, it’s rich for Israel to act appaled by this regardless of its perpetrators given that they struck a school killing a few dozen people in Gaza that same day.