I fully support it deserving a campaign, it really does.
I have thought about this a bit. I think a campaign should follow the timeline; The Timeline of Sins of a Solar Empire II (sinsofasolarempire2.com) in broad strokes. I think it would be good to play as the Traders/TEC for most of it.
Start with a calm map, teach people the basics of the game. At the end, the Vasari arrive. See how not-militarized the Trade Order was, and have a second mission involve the establishment of the TEC. Keep introducing new ships, technologies, abilities etc. The next step is where the Advent get involved. See the TEC get pushed further and further back.
That nicely leads into the first expansion, entrenchment. From there we can go to diplomacy, start to manage each other and the pirates. Then we move onto the split within the factions, and titans. From here we can include other factions. I would put the end point currently at a mixed faction, where the Vasari Rebels take the initiative and lead a part of the TEC that is not hellbent on wiping everyone else out or bunkering down by themselves. The Advent Silent Ones, or a(nother) third subfaction can also come into play here.
Finally, make them escape, right when the secret threat that has been following the Vasari for 10 000 years arrives in Trader space. Or, get that secret threat to the forefront of course.
I'm not a storywriter at all, and I'm not sure on characters or a cohesive plot through the story that is not just the history as stated in the timeline. I think there's a lot fun gameplay there at least, while also teaching people to play and including lore.
Pretty much all the lore can be found here on the website, in the Rebellion manual included with the game and in-game itself (in the form of features, artifacts and descriptions of other gameplay elements).