I never really thought the bars looked broken and considering people tank whole boulders hitting them it’d make sense for Iroh to just tear through. If they were destroyed with firebending tho, it’s not crazy to say Iroh timed it. He’s one of the most spiritually connected people in the entire series and an eclipse probably falls under spiritual event like the solstices do.
Umm the war was absolutely inside ba sing se when iroh first invaded and broke only the outer wall and then again when he retook the city from azulas control
Considering its possible for water benders to blood bend without needing a full moon, i wouldn't be surprised if fire benders can bend during an eclipse. However, the more likely answer is that he just timed it right. He is a master tactician, after all.