It was mentioned in the first video that the henchmen keeping his equipment was a bug/glitch.
I think once you get close enough to the wizard, that is good enough for the guards (if you can easily miss an important NPC, that is a bad design, but once you know who you need to talk to, the game doesn't really need to force that right away).
The barrels there are apparently not private property, so nobody that can see the characters has an objection to them looting.
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