Does Spectral Thief steal boosts from Unburden/Swift Swim/Choice Scarf etc.? Or does it only steal 'normal' boosts, i.e. stat changes?
No, it only steal the normal boosts.
I tested this on Pokemon Showdown. From the replay, you can see Spectral Thief did not steal the boost from Pelipper's choice specs. It also only stole the boost of Agility from Barraskewda. Not scarf or Swift Swim. For Hawlucha, it only stole the boost from Agility again, not the boost from Unburden. Hope this helped.