My take:
This is surely a US-Putin war. Iran is a major supplier of drones for Russia and has a growing armaments capacity, so is a genuine threat to Israel.
Israel is a strong ally of the US. Other economically developed countries in the area sit uncomfortably on a fence. On one hand linked to their neighbours via race (Arab) and religion (Islam). Iran is a bit of an outlier because the people are Persian not Arab, the religion is Shia not Sunni, and also the ayatollahs will not approve of the consumerist mecca (pun not intended) that is Dubai. For the more Gulf states the US and west are where you sell oil, where you gather your affluent tourists and where you gain protection from Russia and other threats. All those officers trained at Sandhurst, arms bought in France, and US bases. At the same time Islam is the glue that unites the people behind the rulers and there will be strong concerns about Israel's action in Palestine.
The US aim will be to destabilise an unpopular Iranian regime. The big question here is, who they are hoping to replace the Ayatollahs with. The regime is very unpopular, particularly amongst the educated middle class, but no organised opposition has been able to develop. The Crown Prince could be used as a figurehead but not more. The hope is that the US have learned from Iraq, where getting rid on Saddam left a dangerous vacuum, but who knows.
The Iranian aim, with these missile attacks will be to loosen Arab logistical support for the US. They are not seeking to hurt civilians, just to hurt the economy with some damage to US bases and aircraft carriers. There will be a lot of talking going on behind the scenes, and until an impasse is reached the attacks will remain low level, though frightening. The UK government will be considering options but shelter in place sounds right for now. If there were to be an escalation it is very likely that the Gulf states would be able to demand a ceasefire to allow evacuation. Iran really does not want to go to war with so many of its neighbours. The aim is to persuade them to support their Muslim brothers over their western economic interests, and thus cut off US support for Israel.