Theocratic Republic might not be the most accurate but I like to imagine the Observance have gained more influence by the time the Bakunin reached a new galaxy
p.s. if any Stellaris players have ideas on how to make other Infinity factions I'd love to hear it
After playing though RT a few times I decided to try out Wrath of the Righteous and as I near the end of my first playthrough I just completed the 'Dance of Maks' dlc content for that game. And I just felt the need to put it out there that I desperately hope we get similar content for Rogue Trader.
For those that don't the Mask dlc for WoTR added a relatively quick side story that occurs just prior to the final dungeon. It gives you a few new types of enemies to fight and more importantly low stakes side quests for each of your companions that let them express their personalities in a context that isn't fighting demons and cultists and a bonus romance scene with whoever your partner is.
After finishing it, I was left craving similar content for the Rogue Trader companions. I quite frankly enjoy the RT companions more than the WoTR ones and it would probably make my year if 'the Infinite Museion', 'Processional of the Damned' or an unlikely 5th dlc adds a mission where each companion gets a new voice acted scene instead of just silent one liners like during the ascension ceremony.