So I noticed that the Neighborhood Contact's missions have little-side quests sometimes. I.e. in one of Operetta's missions there is a bluepill that asks you to plant a bug in the desk of another character. Those side-quests are never mentioned in the mission objectives, and they don't seem to be really relevant either. If you complete them, it doesn't increase the XP or grant you a particular reward. So is there any reason for them to exist or are they there just for the sake of fun?

They are just for fun it's something different; to have a break from regular missions. The Chessman at Tabor Park tells you to go to a contact when you complete his missions though.

Sometimes an NPC will reward you. This one NPC told me to search the filing cabinet for a reward, and it was an item decompiler. I think the dialogue didn't even show up in the completed mission log. No extra XP that i noticed.