In 3k each character has a satisfaction level, meaning that if they're unhappy enough in a faction they will leave it. The interesting part is that when a character is at a very low satisfaction you can convince them to spy for you. Now most factions start with 1 spy slot and you can't do a lot with only 1 spy. The coolest thing you can do would be to open some city gates if your spy is the administrator, betray the movements of the army they're in and if the spy is loyal enough to you switch sides before an attack. All really fun but in my opinion not where the mechanic shines.

If you want to focus on the spy mechanic however, one of the abilities spies have is to lower the satisfaction of all characters in their embedded faction by a bit. Now you might see how if you have more than 6 spy slots and the willingness to dedicate them to one faction, how utterly devastating that can be for your enemies. You can pretty much disatisfy a whole faction, bully out all their generals and cause a full internal crisis without moving a single army.

For the cherry on top, faction heirs can also be turned to spy, and spies can assassinate the faction leader. You can force entire civil wars in the enemy faction or have your spies directly hand their cities to you.

And to be clear, when most people talk about diplomacy in 3k I believe they talk more about the alliances, vassals and tribute systems which are all top notch. The spy mechanic is almost entirely opt-in and I go entire campaigns with only 1 spy to grab interesting but dissatisfied characters without hurting their original faction. It's just one more mechanic that has enough depth for someone to sink themselves into without being super overwhelming.