I'm playing the Until Death Do Us Part mission. I manage to go through undetected, and then the moment I pick up the shard on the desk, I'm automatically detected. All of a sudden people with guns barge into the apartment and I'm in combat with them all at the very instant I touch that shard.

None of the online walkthroughs mention this as a feature of the mission. What is this? Is mine bugged or something?

I remember that gig and that did not happen to me. Certainly is bugged from what you've told us.
Try a earlier save or reloading after restarting the game?