I must admit that I never used the game's Faction rules in my months of playing.
I have a nagging feeling at the back of my mind, however, that I'm missing something by not using them. The way it slots into the Changing the World section seems to indicate that Faction turns+Dominion Changes+Adventuring+Gathering Shards+Dealing with newly created Problems= a Sandbox that pretty much runs itself. Since my prep time is limited AND my player is running a province, the Faction rules are now more relevant than ever.
What are your experiences with the Faction rules? If you use them, would you mind sharing the Faction stats you used? I'm especially interested in stats for the major nations of Arcem.
I tried them, then put them away. I didn't find them as fun as I expected them to be, and it took me more prep time to follow them than do without. I keep a list of factions, estimate roughly how they react to the events taking place, and that's enough for me.
Using them takes some time as it is kind of a game in itself. For a few factions, maybe 3-4 I think it's OK and a game for the GM to play. But with more it gets far too time consuming. The rules work well as guidelines to keep in mind though and can help make on the fly decisions. Adam Koebel has videos of his GM turns for Swan Song where you can see the rules in action to get an idea.
Maybe hack some of the faction mechanics from Scum and Villainy (or Blades in the Dark, which it's based on)?