Outside of some vague details, I've never really been interested in the events that lead up to the Fourth Imperium.
Pournelle's Future History has already come to fruition when the Terrans took over the First Imperium, and the Third Imperium picked up the pieces, even if the cause of the collapse is supposedly financial.
The Confederation is the CoDominium, but on a larger scale. There's a single unified government, but infested with factions, mostly interested in their personal interests, and then that of their constituents.
The fact that the Navy can only build capital ships, and is forced to make up the difference with what we used to call Adventure class ships, is probably to force them to build these ships at local shipyards.
They have strong Home Guard paramilitary units, which they probably will use against their neighbours, much like the rise of nationalism and arms race back on Earth.
Then you have this Supermen coup.
So how will Confederation evolve to the First Empire between now and then? It doesn't really have to.
Like that cat, it can be both states at the same time.l