So, this might be controversial, but I'd like to see Stellaris 2 kind of go off in a completely different direction, because I don't think Stellaris 2 is something that should exist to replace Stellaris 1, and I don't think development on Stellaris 1 should end unless it's in a state where it doesn't need to be replaced.
More Simulation
Paradox games tend to run the gamut between the more boardgame/classic strategy game esque push-button approach of giving the player a lot of direct control and letting them figure out the puzzle and the more simulationist approach where a lot of mechanics are automated to give the impression of a living world that is outside of the player's complete control. Stellaris currently leans a bit more towards the former than the latter, and a lot of people will like that, but personally I'm really curious to see what a more simulationist space 4x game would look like. The pop system has gradually become more automated, for example, but I'd like to see it automated even more, with the player only giving overall directions rather than having a lot of direct control.
More Characterization
Tying into the above, I feel that one issue with the player in Stellaris having so much direct control over its mechanics is that it constantly draws attention back to the mechanics and away from the human scale. I think there needs to be more emphasis on the use of emergent storytelling techniques to characterize the world in which the game takes place (in a way that is also relevant to mechanics, but not purely mechanical). Leaders are a good example. Theme-wise, you've got like maybe a couple of dozen people who are the leading figures in an empire of billions. They should be these huge larger than life characters whose exploits and careers will become part of the history of this galaxy. At the very least, give each one a bio listing their most notable achievements. Describe what their background and personality is like. Give them an RPG-esque skill tree which lets them specialize as they develop experience (with their background and personality perhaps opening new options). Give them medals and awards as they level up and improve. Have events describing their state funerals when they die and have them tracked in a special memorial screen.
But characterization doesn't just have to be for people. When I colonize a planet, I want to get a sense of what it's like to live there and how that's different from living anywhere else. This could mean giving planets more variables beyond just an abstract "type", so we know a bit more about them, adding in more interconnectivity between existing variables (for example, smaller planets should have lower gravity), or even having planets semi-randomly generate a "history" for themselves which affects them in various ways and which the player can then discover. To carry this over into fleets, let each empire field a few experimental or veteran ships which have some extra flavour and add little bonuses to the fleet they're part of, but also incentivize keeping them alive, or let fleets unlock special battle honours or reputations which help to specialize and theme them.
More Diverse Empires "Types" / Less Clear Universal Meta
In Stellaris, most empires play quite similarly, albeit with a unique set of strengths and weaknesses in particular areas. This is great in ensuring the player has a consistent experience and always knows what to do, but it's not so great for narrative because it makes empires feel samey, and it creates a relatively clear and obvious meta.
Pop growth is a good example. It's currently one of the most important stats in Stellaris and having more pops is almost always a good thing. But imagine if that wasn't true. After all, these are futuristic societies where people may not really be interested in reproducing all that much, but maybe as a result the children they do produce are really well educated and given a huge amount of investment, so you end up with a technologically advanced society with a relatively small population but which excels at intellectual pursuits and uses automation to get the most out of its population.
The ideal outcome is that you would end up with a situation where different empires are guided towards pursuing very different playstyles in order to do the thing they excel at. That low population empire might be really dependent on science, for example, because it needs the latest technology to make its small population efficient enough to keep up with growing empires. An authoritarian empire might end up with a huge, bloated population of workers or slaves who contribute little individually because they're an unskilled and impoverished underclass, so the empire needs to keep expanding and growing to avoid falling behind.
More Economy
This sort of ties in with a few of the points made above, particularly the point about characterization. One interesting question might be "what are my miners mining." At the moment, they mine generic minerals, but that's not a particularly satisfying answer. I feel that Stellaris (of all the other Paradox titles) would benefit hugely from a more complex economic simulation, similar to that of Victoria 2. There are so many science-fiction resources and commodities which an empire could produce, and having them makes a lot of other areas more interesting. Planets become more important and unique, for example, because now they might have different resource deposits that you may or may not need.
A deeper economy could also provide a counter to the current principle that tech is king in Stellaris. Maybe the aforementioned low pop high tech empire with huge efficiency needs all these high tech goods and resources to keep the economy going, which means needing to find or import rare resources, while the authoritarians with the huge slave/worker population just need to keep everyone basically fed and have less need to build or import high tech commodities. That's kind of a extrapolation on what already happens, but with more specialized resources it could become challenging enough to source them all that being technologically advanced becomes a choice rather than a necessity. After all, you could just build a lot of low tech ships.
