That first option is indeed the end goal. The problem is that for many decades, the Lebanese armed forces were only the second strongest military within Lebanon. They simply weren’t capable of disarming Hezbollah; if they tried, it would have started a civil war that (barring Israeli intervention) Hezbollah would handily win.
Blowing up Hezbollah cells (that, yes, are intermingled with civilian infrastructure; you can thank Hezbollah for that) and degrading their leadership and fighting capacity has slowly worn Hezbollah down, to the point where they are now at a small fraction of their prior strength and roughly a match for the Lebanese army. Which is why Lebanon has taken monumental and unprecedented steps since this conflict has started, like for the first time ever making it illegal for Hezbollah to shoot rockets into Israel. And then, even more mindblowingly, actually arresting many Hezbollah members (and more since that article was written).
Lebanon’s government obviously can’t say this openly, because there’s a lot of disdain for Israel in Lebanon, but they’ve been cooperating with Israel in these operations because not only do they also want Hezbollah gone (that’s been the case for years, I am sure) but they actually see a path to this goal and are openly working against Hezbollah to make it happen.
How many of those dead were Hezbollah? You don’t think that matters at all? I don’t see how you can possibly say whether or not an action is justified or not without considering whether it targeted militants or civilians.
(Moving to what I hope is the appropriate thread).