Attacking city with Encampment district
The encampment will bombard you with ranged fire as long as you are in range of it, so unless you're confident you can soak the additional damage it's best to position your siege forces on the other side of the city walls where it can't range on you.
As far as I've been able to tell there's no inherent value in taking out the Encampment first other than "it won't be used against me while I'm besieging the city".
Reduce an encampment's defences and take it like a city. At this point the encampment is now "pillaged".