Q.Coral Tree problem
I have a coral tree with beautiful bright orange flowers. However, for the first time in 30 years, it is dropping some kind of weird powdery substance on the ground and table under it. The tree appears to look fine and the substance seems to be coming from the split open seed pods that grow out this time of year after the blossoms are gone and before it drops all of its leaves. I am very sad, as I have lived with this tree 30 years now and it has never had any kind of weakness or pest problem. Any idea what this could be?

I have not been able to find any disease or insect issue for a Coral Tree that would match your description.
I do think you may actually be seeing excess pollen dropping from the plant, which would be perfectly normal.
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm