Since the core mechanic I mentioned is 'Influence', here is a little more about that, although it isn't the first system I started with. Basically, every structure or unit in the map exerts some amount of 'influence' over the hex they occupy, and/or surrounding hexes. As a player, your influence over different hexes is key because it determines not only what area you "own", but also each structure and unit adds/requires influence a little differently, and very few are actually usable with zero influence over a hex.
For example in the image, you can see the castle keep creates an area of concentrated influence around it. So you will have to think about how to place structures to extend your influence towards areas or resources you want to bring within your domain.
Since influence over a hex is tracked for all factions, it is also possible for you to lose control over a hex because an enemy out-influences you. So you may need to take military action!
I was inspired to this mechanic after reading some papers on how cities grow organically to reach out to various resources in their surroundings, instead of just growing in giant blobs, circles, or detached parts, and I wondered how one might replicate that in a builder-game type of setting. I thought influence would be a good way to compel players to target growth towards something, while staying within touching distance.
Please excuse the simple visuals, gameplay before gloss!
P.S. - Extra credit if you can spot one of the bugs visible in this image 🥸