> my impression is that Israel is more concerned with Iran as a general threat
Iran has never attacked Israel unless attacked first. As for their 'proxies' they only really exist because Israel has invaded Lebanon long before Hezbollah existed and its creation was spearheaded primarily by Lebanon's local population as a response to the invasion, with Iranian support.
Iran supports these local 'proxies' because it sees itself as a leader of the Shia and more broadly as a leader of the Muslim world and the Palestinian cause as being the responsibility of every Muslim nation (incl theirs) to get involved with.
Israel is indeed concerned with Iran as a threat, but only because they see the other governments in the region as willing to overlook the Palestinian cause, in exchange for economic links with Israel.
In that sense Iran is very much connected to the Palestinians, this assertion that Iran is just super irrational and wants to see Israel go down because they want to laugh watching it or something is nothing more than cheap Israeli propaganda.
Of course Iran is not just looking for the Palestinians out of altruism, they want a leadership position in the Muslim world and this is their way of gaining legitimacy, but the reason why Israel sees them as a threat is very much because of Iran's interest in the Palestinians.
> Iran has never attacked Israel unless attacked first
Iran was involved in attacks against Israel and Israeli towns in the 1980s and 1990s by their mercenaries in Hezbollah and direct IRGC presence in Lebanon. This happened even when Israel supported Iran during the Iraq-Iran war, so this is strictly not true
Other incidents were the Iranian bombings of the Israeli embassy in Argentine or the Jewish center there, and attempts on the London and Bangkok embassies
Furthermore financing of Hamas during the 1990s suicide campaign with the direct goal of derailing the peace process.
This is part of a long line of Iranian aggressive actions that have led them to being isolated and in a string of wars that greatly destroyed their already diminished economic power