As far as I can tell the stability stat attached to the warden does not contribute in any way to your kingdoms actual stability. The stability stat on your banner just goes up or down based off of if you fail important problem events or not. So if you fail one of the events related to a main quest you'll take a hit, but if you succeed you'll get a boost. Getting to negative BP also seems to give you a hit as well.
The game does explain how BP is calculated very briefly in a popup when you first start your kingdom. It would be nice though if it broke it down in the kingdom screen. The basic formula is just adding up all of your kingdom stat ranks with your economy rank acting as a cap. So if economy is rank 4 then all stats can only contribute 4 points to your BP value no matter their actual rank. Then you add in trade routes and if you're still getting the Brevoy subsidy you divide your generated BP by half and add a flat 30BP to your value.
Overall it's nice that a lot of bugs have been squashed, but the Kingdom management desperately needs a balance pass and advisors need to be looked at again especially the Councillor and Warden positions. Also why on earth is one of the most close minded of your companions (Valerie) a diplomat? Her charisma score isn't based off her personality (if it was I'm sure it would be negative...) but rather because shes supposed to be really pretty.