First of all, your bird was already in some major distress which is why she fell without trying to fly. Egg binding is a life threatening situation, and there is no telling how long she had been in that state. I think when they anesthetized her the first time to remove egg, they should have x-rayed leg then, but if the leg was not at a crooked angle then they probably did not think it was broken. Small hairline fractures can still be there though, so the x-ray was a good idea.
This is a two part situation, and your bird was already in so much distress the second anesthesia did push her over the edge. It is NOT your fault that this happened. Fact is that your bird was likely to die from all this anyway with or without the second anesthesia.
When you get another bird and start having this problem with egg laying, go ahead and take them to the Avian vet for a good overall checkup and for some help in stopping the chronic egg laying. In young birds, not fully developed, egg binding is very common and death from it is just as common. Sometimes, they will let us know they are having problems and sometimes the problem is acute and moves into extreme distress quickly.
I'm very sorry for your loss, and just know that you were trying your very best to help your little bird. Her death hurts you, and it is not your fault, so don't beat yourself up over it. Egg binding is something where we may or may not have any say in the outcome, so you did your best, and that's all we can do. In future, keep in mind about anesthesia and already distressed birds. Vet tried to save her life, and the x-ray should have been done at time of first anesthesia.
Thank you for writing, and we are here to support you anyway we can with any questions you may have in the future.