Internal politics that actually amount to something more than having faction giving some influence or not giving it if they don't endorse your rulership. Since I love to play authoritarian regimes, I'd like to use the army and the fleet to suppress the equal rights faction every now and then, instead of having always to conquer my neighbors.
Also I'd like the possibility to flesh out the state ideology and religion, something like the religion of CK3, to make actually empires different from each one beside their founder race when they share a similar ideology.
Another thing I would really like as a game mechanic would be adding more depth to the monarchy, having more possible heirs to select, the occasional popular brother that want to usurp the throne and things that spice a litte up the institution.
The possibility to play a resurgent precursor civilization that wants to put the upstart new species in their place.
The possibility to integrate the Federation members in your empire with peaceful means, of using cultural influence to change the ideology and religion of other states, pretty much waging cultural wars beside the regular ones.
And I like to see implemented a simplified systems for the pops: for example, when a planet has reached the max population, instead of creating more pops on said planet, that have to be resettled manually, the excess population should translate in a faster population growth for that species on colonies, to simulate the migration from overpopulated worlds to new ones, without player involvement every single time. After all, if a species has a free migratory policy, citizens should take advantage of the free land, better jobs and so on if available.