I think that the text is quite clear that it is not the Paternova that provides the Astronomican, only that whomever happens to be the Paternova
somehow improves the abilities of the Navigators within their genetic line. No suggestion is made as to how this might be possible, though I wouldn't be surprised if they were somehow going down the
Dune route. (Or even trying to mix it up by making it all Bene Gesserit with racial memory and empowerment.)
Again, not improving the Astronomican, but improving the basic abilities of the Navigators of their line.
I also have strong doubts that the Paternova is any part of the Emperor's soul, or that the Paternova is an avatar/daimon (deliberate spelling of that last) of the Emperor or Star Child. Then again, what's one more "conspiracy theory," as Irandura would have it?
(And it's certainly no worse than speculating whether the Soul Binding might also be a means of either extending sections of the Many Mind of the Emperor, or as a means of perpetuating said entities "overwatch" on the Imperium. Perhaps it's just as crazy, though?
)
It would be interesting to speculate a mechanic by which the Paternova's abilities enhance those of their line, though.
Kage