All correct.
However, you have to recall, with these “guys” everything is personal. They change alliances over time. And as to who is a “God of Chaos” or a “God of Law” that is something of a matter of both perspective and circumstance. There are “people” who are permanently in the Chaos camp, there are many more who become aligned with it for their own purposes for various periods of time. The three gods at the end of Book III should not be considered a full set. It’s just a group of collaberators on a particular project, each with their own goals which happen to cross paths.
(such projects can easily last hundreds, even thousands of years–which are very small time frames for immortals. If you live, conservatively, to be 100,000 years old. Working with some other god for 1,000 years is like 1 year of your life at most. If a god typically phoenixs every 2 or 3 hundred thousand years, then a 1,000 year collaboration is like a six month or less gig).
AND ALSO “now” is later. Everything people from ‘Earth’ know about the Egyptian gods has already happened. Same with the Aesir. In fact, by the time the Earth scandinavians like Ragnar Lothbrook were going a viking, Ragnarok was old news, the Ásbrú was shattered, they were worshipping their ancestors’ gods.
The “gods of Egypt” are so (currently) out of the picture, that Ramses the archdemon (The Damned/The Great/The Second) is so convinced that his old gods are toast, that he doesn’t even recognize Bess,his coconspirator to get the book, as Bastet from his home world.
FYI I should point out that Astet (Isis) is a member of the Nyjyr Ennead, and thus nominally allied with Tommus, which puts her squarely against Set. And all of this ties out to why and who shafted the Nyjyr Ennead in Astlan, and (elsewhere) and why they are living in Exile (a.k.a. hiding)