I don't think your president being a moderate has any implications since the supreme leader is where the power lies. All of the presidential candidates that were allowed to run during this last election were approved by the supreme leader. I think the supreme leader and Irans ruling elite are smart enough to have hardline voices and moderate voices to try and appease the people there. Nothing better than having two conflicting messages that only disagree on a surface level.
That said, the fact that Masoud Pezeshkian was allowed to run and win to me means that Khamenei wants to cool international tensions and try neogiations for a bit.
All of that said though, Israel doesnt care about any of this because very powerful parts of their government not only want all out war, but want to draw the US into a conflict.
The war against Hamas is starting to cool down and the war hawks are getting restless. No way a govt can give the order to assasinate the person they were negotiating a peace deal with. All reports was that the cease fire was getting close and then they kill their chief negotiating partner. That makes no sense other than parts of the govt don't want peace and they are were the power lies.
Imo the end goal for Israel is that they clear out and annex Gaza, and then invade Lebanon and occupy southern Lebanon and begin to settle it. They will try to have their war continue and continue poking Hezbollah and Iran until this happens.
Also I agree Iran wont truly respond because an all out war with Israel does not benefit it at all. Israel is more powerful technologically and economically, but more importantly, a war against Israel would be like 10 vs 1 with Iran fighting against the West as well, and Iran is too smart to let that happen.