Often the offices for visas or papers is near the street or parking area. Then you have a garden etc before you go into the embassy proper.
When I adopted my boys in Colombia 40 years ago, a car bomb was placed near the visa office, killing one applicant sitting near the door. But it was no where near the embassy itself, which had several more layers of security.
Ditto for here in the Philippines where demonstrations by leftists and explosive devices placed by Islamic terrorists happen a couple times a year. Missiles and drones however are a harder threat to stop.
During the war, US personnel were frequently hit by missiles aimed to inside the us zone, but rarely reported in the news.
Trump is sending a message...you hit us and we hit you back.
Of course, the Iranians will embed wives and children or hide in civilian areas to show dead bodies to the MSM, just as they do in Israel or in Yemen, and the MSM will echo the anti American protest while ignoring atrocities by the Iranian backed terror groups.
Trump
You described perfectly the outer appearance of the Baghdad compound. Almost a darkened unmanned movie theater ticket box looking affair. Windows to bang on, but seemingly leading to nowhere, and a nearby vehicle gate in the outer wall. But that place is a fortress, being in a perpetual war zone.
This flock of demonstrators, in their current form, with their shirt tails hanging out and a can of lighter fluid are no match for that fortress wall.
I do see what you mean about the receiving areas in embassies being subject to risk when caught on a normal access day.