I do want to stress that to me the part of Rogue One’s DNA that translates over into Andor isn’t just the visual aesthetics or surface tone. When I talk about its “geopolitical texture”, it’s in how:

Jedha is understood and talked about as an ongoing warzone. The franchise typically conceptualizes war as skirmishes beginning and ending in an afternoon, so much so that we have signifiers like BBY to denote the Death Star run that was over in 20 minutes. We visit Jedha as a place that more or less carries on in the midst of heightened tensions, until it doesn’t.
The Alliance conceptualized as different factions, and rebels as a whole having diverse ideologies. Saw as an “extremist” compared to Yavin’s cell is a broad example, but it’s there - and there’s also just subtle flourishes to the in-universe speak that maintains The Empire as an Establishment over this revolution. The Rebels are typically understood almost as its own secret pseudo-government/military, but so much of Rogue One’s first acts emphasizes how beholden they still are to Imperial law, and how fragile whatever authority over their people actually is.
Careerism in the Imperial ranks is given grounded play here. Between Krennic and Tarkin, but also in the Ersos’ blurred professional/personal relationship to Krennic, particularly what’s suggested in the Republic/Empire transition period. Catalyst is a pretty good book so maybe some of that is leaking into my appreciation here, but Rogue One still provides the space for this kind of detailed worldbuilding, and services more grounded drama than melodrama.

And then there’s other stuff that just fills out the world far more thoughtfully than we’ve gotten from the franchise recently. The Whills as a non-Jedi institution that has their own, non-instrumental relationship with the Force is a great concept! I’m not saying it gets to really dig into these things, but it’s coming at it exactly how Andor did. And when I say “seriously” I’m NOT talking about tone or grit or darkness, but in how it lacks pretension and cynicism. It’s all about buying into this Star Wars thing like it was a derived from a sci-fi TTRPG guidebook; nerdy engagement with a fixed, detailed lore, blowing up an aesthetic element and giving it logistical play. Pretending this was all real, and that it should feel real, and be handled like it was real material. Not winking at the conventions that betray that illusion through whimsy and one liners.

It’s not about What Would George Lucas Do, it’s unconcerned with reacting to questions of What Is The Spirit or “Soul” of Star Wars? None of that genre-play or legacy-posturing. Just being a movie. It can be dry because of it, and it’s absolutely mashed together with a more traditional Star Wars third act, but I really do think it’s all there in the macro.