Hezbollah started limited attacks after Israel starting bombing Gaza. That was the level of engagement for many months. The understanding to keep it at that level changed with Israel escalating into Syria and Lebanon more and more, as well as the total annihilation they bring on Gaza.
You don't need to look at all of the "conflict". However the fundamentals are not complicated. Israel is a settler colonial state. It is found on and will be completed by genocide and ethnic cleansing of the population it is stealing the land from. This is what happened in what is today the US. This is what France tried in Algeria. And you find this again and again throughout human history.
You can engage in all sorts of debates as to who has shot first at what point, but this fundamental structure of the situation does not change.
Hezbollah made it clear they don't want an escalation and the way to end the fighting and the border is by Israel ending the genocide in Gaza. The same goes for the regime in Iran, which had to respond to Israels assault on the embassy, but they did so in a matter to show force, without causing relevant damage. The one escalating is Netanyahu, who hopes to draw all of the west into a total war in the middle east, because the support for his genocide is dwindling.
It is the mindset of a schoolyard bully, that always picks fights, to then call on his bigger brother to defend him. It would be funny, if it wouldnt be a genocidal maniac, that is set to put the lives of hundreds of millions of people at risk.
So they want to install a puppet "ruling" over the rubble to help finish the handover to the genocidal maniacs.