I don't know if you guys think the same but In a 4X immersion factors can be sparse, especially in custom games with no official story line.
One thing that works pretty well for me is when the AI leaders have a lot of personality. In GalCiv 2 they are quite interesting and I do like when you are interrupted by a Civ leader telling you that you should work together plotting against another Civ, or when they tell you that they just made breakthrough X etc.
I think it would be nice if this concept was expended with more diverse and interesting communications, and more frequent.
I am currently playing a game as Yor and I disabled tech trading. I used to communicate with other civs all the time to trade techs but in this game I have almost no contacts and it feels weirdly empty because of it. ( although this fits the Isolationist Yor theme )
I miss having news of Kona talking me about tasty Torian skin and the dominion of Korx telling me about their skull collection.
Since GalCiv is a rather humorous game It would be somewhat easy to pepper it with various interactions between civs that take place in the diplomacy screen. I am thinking about something in the style of Jagged Alliance. Some Ai leader commenting on something you have just done in a positive or negative way or maybe hinting you of how their relation with other civs fluctuate.
For exemple suppose relation between Terran and Thalan just got worse, Terran might chime in and complain they cannot stand Body odor of the Thalan or something else silly like that.
It could be used to highling the lore of the GalCiv universe, like Drengin congratulating you after you conquered a Torian planet etc.
In Sword of the Stars the AI civs could be interesting when you were allied with them they could comment on things like your ability to play and they would tell you which planet they needed help defend of wanted to capture. You could also open the diplo screen simply to insult them, which I think served no purpose beside worsening your relations but I liked it very much.