“Egypt thinks they own all the warer and has refused to negotiate. This is a problem that can be resolved but for Egyptian recalcitrance.”
Doesn’t matter, at this point. Egypt has 100M people now, and 98% (or whatever) of their water is from the Nile. If a ‘solution’ to this issue is not found, it’s difficult to see Egypt (or any other government in a similar situation) not go to war.
The dam can be completely filled in anywhere from three to ten years. Obviously, Ethiopia, which faces periodic famine due to drought, would like it sooner. Ethiopia has offered to share the power generated with Sudan and Egypt. If I recall, Israel has offered to help Egypt with the water problem, probably by building desalinization plants. Egypt does have several options that will minimize the impact, but the government simply wants to keep things the way they are now. When the British controlled the headwaters they agreed to not dam the river, giving Egypt veto power over any projects. That was nearly a century ago.
If the Ethiopian government does not fill up the dam, then they will probably be replaced by a government that will. The present government has been, apparently, very reasonable. But they have also placed anti-air weapons around the dam and they have to answer to people who face starvation. (I looked at photos of the antiair weapons. Egypt probably wouldn’t lose any planes to them. However, bombing a dam that has been more than a decade in development would probably cause them diplomatic headaches. Also, it’s entirely possible that trying to destroy it and failing would be a disaster.)
If cutting off the flow of water into another country is a cause of war, you should see the Rio Grande as it goes into Mexico. See the link.
https://www.theguardian.com/environment/2021/jan/12/rio-grande-new-mexico-river-water