After reading this thread, I had an idea on how culture-focused strategy stages might look like (at least the ones after Awakening): what if we shifted the focus onto the culture editor, and made it an active part of the stage?
The gist is, the editor would be more of a control interface than just an editor; the player would be able to take actions through the people of their culture. Settling new land, establising trade routes, building buildings, inciting rebellions against states that have subjugated your culture. Or even states of your own culture, that, for one reason or another, are disadvantageous to your strategy.
In a way, the framing of these actions as done by the culture, and not by the state, like in most strategy games, might be a better one. Migrations to Brittany, trade, the Viking conquests/trade/migrations*, most pre-modern production, etc. weren’t necessarily directed by states, but by groups of people, with no political power.
* The Viking conquests were more complicated than that, in my understanding, but they weren’t connected to a single state. Though they were sometimes done by members of the nobility.
Of course, we shouldn’t diminish the influence that a state has. The Republic of Venice conquered territories and negotiated quarters in Mediterranean cities with the purpose of protecting trade; many medieval countries regulated production/trade through monopolies, etc. That influence would add another dimension to the game, because not only would the player have to struggle against other cultures, but also against states.
In addition, many building projects were directed by states. Such as castles, aqueducts, roads, etc. Cities were, too, sometimes founded by states (e.g. Lugdunum). That’s something to keep in mind.
Now, to address the elephant in the room. Do I think that the player should be able to control states of their own culture? Probably yes, but not while being in the “culture editor”. Just like in our current stages the player can control both the entire species and individual bacteria, but not at the same time. So, maybe the player could choose to “possess” states, and play as their rulers, and return back to the “culture editor” at will.
We need to take care not to make it seem like the culture that the player controls is a hivemind or some sort of shadow government. One way to do that is to make actions more like nudges, rather than direct decisions. Instead of building a mine, the player would encourage mining activities in a town; instead of starting a revolt, the player would sow discontent and make the population of a province more likely to rise up; instead of founding a city, the player would direct migrations to a location, or establish trade routes over that place, making it a good spot for a city to be founded. So, the player would basically be in control of a collective consciousness; not controlling individual people, but directing masses of people towards a desired outcome.