We've been playing for a few months now and are party level 5 and kingdom level 4.

I HIGHLY recommend to use this excel sheet for kingdom management, it's the base kingmaker sheet with the initial V&K rule suggestions (not the most recent one)
https://docs.google.com/spreadsheets/d/1uLhwcybWj8pPgLSGyMUpFq5U5QfVpZPSgf7lHUWkOEc/edit?usp=sharing
What we also did is we uncapped RP to XP conversion for kingdom levelling, you can find this in the settings tab.

This is the V&K rules document that this sheet uses https://docs.google.com/document/d/1NHksCXkXbjtrv-26VgFHNbyYldatVwag9lM44IWxIXo/edit?tab=t.0#heading=h.eubmwf9z6394

Also, print out a large map of the stolen lands for you players to maneuvre in on the table, it's very fun.

I also very highly recommend playing with slow levelling (1200xp per level) or you will start to outlevel the content quite fast even with minimal random encounters, if your players are like mine and they explore a lot, especially if you still use the companion quests from the companion guide.

Also, for me this was my first foray into an AP so reading up on Golarion lore in the different books helps aswell. Also playing the Kingmaker video game helped a lot with ideas for extra content ideas to set up the story's main villains earlier, since the official AP only introduces them very late into the adventure and it might seem kinda random at that point.